# Publications

Journal papers:

1980
1. On the symmetric and Rees algebra of an ideal generated by a d-sequence, J. Algebra 62 (1980), 268-275.

2. 1981
3. The perfection of Buchsbaum-Eisenbud varieties and generic modules of projective dimension two, Trans. Amer. Math. Soc. 265 (1981), 211-233.
4. On the symmetric algebra of a module, J. Algebra 69 (1981), 113-119.
5. Powers of Ideals generated by weak d-sequences, J. Algebra 68 (1981), 471-509.
6. Symbolic powers of prime ideals and special graded algebras, Comm. in Algebra 9(4) (1981), 339-366.
7. A characterization of locally Cohen-Macaulay completions, Pac. Jour. of Math. 94 (1981), 131-138.
8. Almost complete intersections and factorial rings, Jour. of Algebra 71 (1981), 179-188.

9. 1982
10. The theory of d-sequences and powers of ideals, Advances in Mathematics 46 (1982), 249-279.
11. On the associated graded algebra of an ideal, Illinois Jour. of Math. 26 (1982), 121-137.
12. Symbolic powers of primes and weak d-sequences, Proc. of the Algebra Conf., George Mason University, 1979, Marcel Dekker 68 (1982), 173-200.
13. Linkage and the symmetric algebra of ideals, A.M.S., Proc. of the Jacobson Conf., eds. S. Amitsur, D. Saltman, and G. Seligman, Contemporary Mathematics 13 (1982), 229-236.
14. On the finite generation of symbolic blow-ups, Math. Zeitschrift 179(1982), 465-472.
15. Graded rings associated to an ideal, Conf. on Commutative Algebra, Katata, Japan, ed. by H. Matsumura, Proceedings of the Ninth Taniguichi Symposium (1982), 15-19.
16. A remark concerning multiplicities, Proc. Amer. Math. Soc. 85 (1982), 331-332.
17. On the normality of Schubert varieties (with V. Lakshmibai), Proc. Indian Acad. Sc. 91 (1982), 65-71.
18. Linkage and the Koszul homology of ideals, Amer. J. Math. 104 (1982), 1043-1062.

19. 1983
20. Cohen-Macaulay Rees algebras and their specialization (with D. Eisenbud), Journal of Algebra 81 (1983), 202-224.
21. Strongly Cohen-Macaulay schemes and residual intersections, Trans. Amer. Math. Soc. 277(2) (1983), 739-763.
22. Invariants of liaison, Proceedings of the Third Midwest Algebraic Geometry Conference, ed. by I. Dolgachev, Ann Arbor, Springer-Verlag Lecture Notes in Math. 1008 (1983), 65-74.

23. 1984
24. Numerical invariants of liaison classes, Inventiones Math. 75 (1984), 301-325.

25. 1985
26. The Koszul homology of an ideal, Advances Math. 56 (1985), 295-318.
27. Deformations and divisor class groups (with B. Ulrich), Amer. J. Math. 107 (1985), 1265-1303.
28. A characterization of Kempf varieties by means of standard monomials and the geometric consequences (with V. Lakshimibai), J. Algebra 94 (1985), 52-105.
29. Complete local domains of type two are Cohen-Macaulay (with D. Costa and M. Miller), Bulletin London Math. Soc. 17 (1985), 29-31.
30. Criteria for complete intersections, J. London Math. Soc. 32 (1985), 19-30.
31. A note on the multiplicity of Cohen-Macaulay algebras with pure resolution (with M. Miller), Canadian J. Math. 37 (1985), 1149-1162.
32. A criterion for intersection multiplicity one (with R. Achilles and W. Vogel), Nagoya Math. J. 100 (1985), 49-63.

33. 1986
34. Dimension and components of symmetric algebras (with M. Rossi), J. Algebra 98 (1986), 200-210.
35. Liaison of monomial curves in P3 (with H. Bresinsky), J. fur die reine und Angewandte Math. 365 (1986), 33-66.
36. Some dimension three cases of the canonical element conjecture (with J. Koh), Proc. Amer. Math. Soc. 98 (1986), 394-398.
37. A criterion for spots (with W. Heinzer and J. Sally), Kyoto J. Math. 26 (1986), 667-671.
38. Determinantal ideals of linear type, Archiv. der Math. 47 (1986), 324-329.
39. Integral closures and primary components of ideals in three dimensional regular local rings, Math. Annalen 275 (1986), 617-635.
40. Unmixed ideals in 3-dimensional regular local rings, Atas da 9a Escola de Algebra, (1986), 5-24.

41. 1987
42. The structure of linkage (with B. Ulrich), Annals of Math. 126 (1987), 277-334.
43. Hilbert functions and symbolic powers, Michigan J. Math. 34 (1987), 293-318.

44. 1988
45. Birational extensions in dimension two and integrally closed ideals (with J. Sally), J. Algebra 115 (1988), 481-500.
46. Minimal linkage and the Gorenstein locus of an ideal (with B. Ulrich), Nagoya J. Math. 109 (1988), 159-167.
47. Algebraic linkage (with B. Ulrich), Duke Journal of Mathematics 56 (1988), 415-430.
48. Tight closures of ideals (with M. Hochster), Bulletin Amer. Math. Soc. 18 (1988), 45-48.
49. Residual intersections (with B. Ulrich), J. fur die reine und Angewandte Math. 390 (1988), 1-20.

50. 1989
51. Reduced normal cones are domains (with A. Simis and W. Vasconcelos) Contemporary Mathematics 88 (1989), 95-102.
52. Complete ideals in two dimensional regular local rings, Commutative Algebra, Math. Sci. Research Inst. Publ. 15 (1989), 325-338.
53. Powers of Licci ideals (with B. Ulrich), Commutative Algebra, Math. Sci. Research Inst. Publ. 15 (1989), 339-346.
54. Tight closure (with M. Hochster), Commutative Algebra, Math. Sci. Research Inst. Publ. 15 (1989), 305-324.
55. Tight closure and strong \$F\$-regularity (with M. Hochster), Mèmoire de la Societè Mathèmatique de France 38 (1989), 119-133.

56. 1990
57. Tight closure, invariant theory, and the Briançon-Skoda theorem (with M. Hochster), J. Amer. Math. Soc. 3 (1990), 31-116.
58. Zeros of differentials along one-fibered ideals (with R. Fedder and R. Hübl), Proc. Amer. Math. Soc. 108 (1990), 319-326.
59. On the vanishing of local cohomology modules (with G. Lyubeznik), Inventiones Math. 102 (1990), 73-93.
60. Generic residual intersections (with B. Ulrich), Commutative Algebra Proceedings: Salvador, Lecture Notes in Mathematics 1430 (1990), 47-60.
61. Ideals with a regular sequence as syzygy, in Appendix to: A Beauville, Sur l es hypersurfaces dont les section hyperplane sont á modulo censtant \inbook Grothendieck Festschrift I (with D. Eisenbud) (1990), 121-132.

62. 1991
63. Tight closure and elements of small order in integral extensions (with M. Hochster), J. Pure Applied Algebra 71 (1991), 233-248.
64. Cofiniteness and vanishing of local cohomology modules (with J. Koh), Math. Proc. Camb. Phil. Soc. 110 (1991), 421-429.
65. Absolute integral closures are big Cohen-Macaulay algebras in characteristic p (with M. Hochster), Bull. Amer. Math. Soc. 24 (1991), 137-143.
66. Absolute integral closure and big Cohen-Macaulay algebras, Proc. of the International Congress of Math., Kyoto, 1990, Vo. l I, Math. Soc. of Japan (1991), 339-349.

67. 1992
68. Almost complete intersections (with J. Koh), J. Algebra, 145 (1992), 22-31.
69. Powers of ideals having small analytic deviation (with S. Huckaba) Amer. J. Math. 114 (1992), 367-403.
70. Infinite integral extensions and big Cohen-Macaulay algebras (with M. Hochster), Annals Math. 135 (1992), 53-89.
71. On the structure of certain normal ideals (with B. Ulrich and W. Vasconcelos), Compositio Math. 84 (1992), 25-42.
72. Direct methods for primary decomposition (with D. Eisenbud and W. Vasconcelos), Inventiones Math. 110 (1992), 207-236.
73. Local properties of Licci ideals (with B. Ulrich), Math. Z. 211 (1992), 129-154.
74. Uniform bounds in noetherian rings, Inventiones Math. 107 (1992), 203-223.
75. Problems in local cohomology, Free Resolutions in Commutative Algebra and Algebraic Geometry Sundance 90, Res. Notes in Math., Jones and Barlett 2 (1992), 93-108.
76. Degeneracy of Schubert varieties (with V. Lakshimibai), Contemporary Math. 139 (1992), 181-235.

77. 1993
78. Rees algebras of ideals having small analytic deviation (with S. Huckaba) Trans. Amer. Math. Soc. 339 (1993), 373-402.
79. Bass numbers of local cohomology modules (with R. Sharp) Trans. Amer. Math. Soc. 339 (1993), 765-779.
80. Phantom homology (with M. Hochster), Memoirs Amer. Math. Soc. 490 (1993).
81. Localization of tight closure and modules of finite phantom projective dimension (with I.Aberbach and M. Hochster), J. reine u. Angew. Math. 434 (1993), 67-114.
82. Hyperplane sections of algebraic varieties (with B. Ulrich) Journal of Algebraic Geometry l2 (1993), 487-505.
83. An improved Briançon-Skoda theorem with applications to the Cohen-Macaulayness of Rees algebras (with I. Aberbach) Math. Annalen 297 (1993), 343-370.

84. 1994
85. A quick proof of the Hartshorne-Lichtenbaum vanishing theorem (with M. Brodmann), Algebraic Geometry and Its Applications, Springer-Verlag, New York-Berlin, (1994), 305-308
86. Tight closure of parameter ideals and splitting in module finite extensions (with M. Hochster), Journal of Algebraic Geometry, 3 (1994), 599-670.
87. Canonical modules and connectedness (with M. Hochster), Contemporary Math. 159 (1994), 197-208.
88. Torsion in tensor products and the rigidity of Tor (with R. Wiegand) Math. Annalen, 299 (1994), 449-476.
89. F-regularity and smooth base change (with M. Hochster), Trans. Amer. Math. Soc. 346 (1994), 1-60.

90. 1995
91. Reduction numbers, Rees rings, and Pfaffian ideals (with I. Aberbach and S. Huckaba), J. Pure Applied Algebra 102 (1995), 1-16.
92. Core of ideals in two-dimensional regular local rings (with I. Swanson), Michigan J. Math. 42 (1995), 193-208.
93. Reduction numbers, Briançon-Skoda theorems and the depth of Rees algebras (with I. Aberbach and N.V. Trung), Compositio Math. 97 (1995), 403-434.
94. Applications of the existence of big Cohen-Macaulay algebras (with M. Hochster) Advances Math. 113 (1995), 45-117.
95. Residual intersections and the number of equations defining projective varie ties (with H. Martin), Communications Alg. 23 (1995), 2345-2376.
96. On reduction exponents of ideals with Gorenstein formring (with M. Herrmann and J. Ribbe), Proc. Edinburgh Math. Soc. 38 (1995), 449-463.

97. 1996
98. A theorem of Briançon-Skoda type for regular local rings containing a field (with I. Aberbach), Proc. Amer. Math. Soc. 124 (1996), 707-714.
99. A tight closure approach to arithmetic Macaulayfication (with I. Aberbach and K. Smith) Illinois J. Math. 40 (1996), 310-329.
100. On the structure of Gorenstein ideals of deviation two (with B. Ulrich and W. Vasconcelos), Results in Math. 29 (1996), 90-99.

101. 1997
102. Gaussian polynomials and content ideals (with W. Heinzer), Proc. Amer. Math. Soc. 125 (1997), 739-746.
103. Tight closure and the Kodaira vanishing theorem (with K. Smith), J. fur die reine und Angewandte Math. 484 (1997), 127-152.
104. The height of ideals and regular sequences (with V. Trivedi), manu. math. 93 (1997), 137-142.
105. Tight closure and strong test ideals, Jour. Pure Applied Algebra 122 (1997), 243-250.
106. Tensor products of modules, rigidity, and local cohomology (with R. Wiegand), Math. Scand. 81 (1997), 161-183.

107. 1998
108. Integral closures of ideals (with A. Corso and W. Vasconcelos), manu. math. 95 (1998), 331-348.
109. The Dedekind-Mertens lemma and the content of polynomials (with W. Heinzer), Proc. Amer. Math. Soc. 126 (1998), 1305-1310.
110. Symbolic squares in regular local rings (with J. Ribbe), Math. Z. 229 (1998), 31-44.
111. A generalized Dedekind-Mertens lemma and its converse (with A. Corso and W. Heinzer), Transactions Amer. Math. Soc. 350 (1998), 5095-5109.

112. 1999
113. Normal ideals in regular rings (with Sam Huckaba), J. reine angew. Math. 510 (1999), 63-82.
114. Hyman Bass and Ubiquity: Gorenstein Rings, Contemporary Math. 243 (1999), 55-78.

115. 2000
116. A cancellation theorem for ideals, J. Pure Applied Alg. 152 (2000), 123-132.
117. Desingularizations and the uniform Artin-Rees theorem, J. London. Math. Soc. 62 (2000), 740-756.
118. Test exponents and localization for tight closure (with M. Hochster), Mich. Math. J. 48 (2000), 305-330.
119. The saturation of Frobenius powers of ideals, Comm. Alg. 28 (2000), 5563-5572.
120. Introduction to the collected papers of Joseph Lipman, Queen's Papers in Pure and Applied Mathematics, 117 (2000), 1-12.

121. 2001
122. Vanishing theorems for complete intersections (with D. Jorgensen and R. Wiegand), J. Alg. 238 (2001), 684-702.
123. Fiber cones and the integral closure of ideals (with R. Hübl), Collect. Math. 52 (2001), 85-100.
124. F-rational rings and the integral closure of ideals II (with I. Aberbach), in 'Ideal Theorectic Methods in Commutative Algebra,' edited by D. Anderson and I. Papick, (2001) 1-12, Marcel Dekker, New York.
125. F-rational rings and the integral closure of ideals (with I. Aberbach), Mich. J. Math. 49 (2001), 3-11.
126. A simple proof of some generalized principal ideal theorems (with D. Eisenbud and B. Ulrich), Proc. Amer. Math. Soc. 129 (2001), 2535-2540.

127. 2002
128. Unmixed local rings with minimal Hilbert-Kunz multiplicity are regular (with Y. Yao), Proc. Amer. Math. Soc. 130 (2002), 661-665.
129. Comparison of symbolic and ordinary powers of ideals (with M. Hochster), Invent. Math. 147 (2002), 349-369.
130. Two theorems about maximal Cohen-Macaulay modules (with G. Leuschke), Math. Annalen 324 (2002), 391-404.
131. The Tor game (with R. Wiegand), Commutative Ring Theory and Applications by Marco Fontana, Salah-Eddine Kabbaj, and Sylvia Wiegand Lecture Notes in Pure and Applied Mathematics, 231, (2002), 289-300.

132. 2003
133. What is the Rees algebra of a module? (with D. Eisenbud and B. Ulrich), Proc. Amer. Math. Soc. 131 (2003), 701-708.
134. Special tight closure (with A. Vraciu), Nagoya Math. J. 170 (2003), 175-183.
135. Local rings of countable Cohen-Macaulay type (with G. Leuschke), Proc. Amer. Math. Soc. 131 (2003), 3003-3007.
136. Symmetry in the vanishing of Ext over Gorenstein rings (with D. Jorgensen), Math. Scand. 93 (2003), 161-184.

137. 2004
138. Vanishing of Ext and Tor over some Cohen-Macaulay local rings (with L. Sega and A. Vraciu), Illinois J. Math. 48 (2004), 295-317.
139. Heights of ideals of minors (with D. Eisenbud and B. Ulrich) Amer. J. Math. 126 (2004), 417-438.
140. On a conjecture of Auslander and Reiten (with Graham Leuschke) J. Algebra 275 (2004), 781-790.
141. Hilbert-Kunz functions for normal rings (with M. McDermott and P. Monsky) Math. Res. Letters 11 (2004), 539-546.
142. Order ideals and a generalized Krull height theorem (with D. Eisenbud and B. Ulrich) Math. Annalen 330 (2004), 417-439.

143. 2005
144. On the core of ideals (with N. V. Trung) Compositio Math. 141 (2005), 1-18.
145. Fitting ideals and finite projective dimension (with D. Jorgensen and D. Katz) Math. Proc. Camb. Phil. Soc. 138 (2005), 41-54.
146. Some criteria for the Gorenstein property (with D. Hanes) J.Pure Applied Alg. 201 (2005), 4-16.
147. Approximations of infinite resolutions (with David Eisenbud) J. Pure Applied Alg., 201 (2005), 284-294.

148. 2006
149. Integral closure of ideals and annihilators of homology ((with A. Corso, D. Katz, and W. Vasconcelos) Lect. Notes Pure Appl. Math., Chapman and Hall/CRC, 244 (2006), 33-48.
150. Regularity of Tor and graded Betti numbers (with D. Eisenbud and B. Ulrich) Amer. J. Math. 128 (2006), 573-605.
151. Frobenius test exponents for parameter ideals in generalized Cohen-Macaulay rings (with M. Katzman, R. Sharp, and Y. Yao) J. Alg. 305 (2006), 516-539.
152. Rings that are almost Gorenstein (with A. Vraciu) Pacific J. Math. 225 (2006), 85-102.

153. 2007
154. Absolute integral closure in positive characteristic (with G. Lyubeznik), Advances Math. 210 (2007), 498-504.
155. Ideals defining Gorenstein rings are (almost) never products, Proc. Amer. Math. Soc. 135 (2007), 2003-2005.
156. Liaison of monomial ideals (with B. Ulrich), Bulletin London Math. Soc. 39 (2007), 384-392.
157. Correction to 'Tensor products of modules and the rigidity of Tor' (with R. Wiegand), Math. Annalen 338 (2007), 291-293.
158. Lectures on local cohomology (with an appendix by Amelia Taylor), Cont. Math. 436 (2007), 51-100.
159. Fine behavior of symbolic powers of ideals (with M. Hochster), Illinois J. Math. 51 (2007), 171-183.
160. Minimal homogeneous liaison and licci ideals (with J. Migliore, U. Nagel, and B. Ulrich), Cont. Math. 448 (2007) 129-139.

161. 2008
162. F-thresholds with applications to integral dependence and multiplicity (with M. Mustata, S. Takagi, and K. I. Watanabe), Michigan Math. J. 57 (2008), 463-483.
163. Mathematical biography of Melvin Hochster, Michigan Math. J. 57 (2008) (v)-(ix).

164. 2009
165. On the support of local cohomology (with D. Katz and T. Marley), J. Algebra, 322 (2009), 3194-3211.
166. Quasilength, latent regular sequences and the content of local cohomology (with M. Hochster), J. Algebra, 322 (2009), 3170-3193.
167. Uniform equivalence of symbolic and adic topologies (with D. Katz and J. Validashti), Illinois Journal of Mathematics, 53 (2009), 325-338.

Other publications
1. An algebraist commuting in Berkeley, Math. Intelligencer 11(1) (1989), 40-52.

Edited books
1. Commutative Algebra, edited with M. Hochster, J. Sally, Math. Sci. Research Inst. Publications 15 (1989), Springer-Verlag, New York.
2. Free Resolutions in Commutative Algebra and Algebraic Geometry, Sundance 90, edited with D. Eisenbud, Research Notes in Mathematics 2 (1992), Jones and Bartlett Publishers, Boston, London.
3. Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra, Contemporary Math., edited with William Heinzer and Judith Sally, 159 (1994), American Mathematical Society, Providence.
4. Trends in Commutative Algebra, edited with L. Avramov, M. Green, K. E. Smith, and B. Sturmfels, Math. Sci. Research Inst. Publications 51 (2004), Cambridge University Press.

Books
1. Tight Closure and its Applications, CBMS Lecture Notes 88 (1996), American Mathematical Society, Providence.
2. Integral Closure of Ideals, Rings, and Modules (with I. Swanson), London Math. Soc. Lecture Note Series 336 (2006), Cambridge University Press.