# Joseph Lipman

**Professor Emeritus**

###### Research Interest(s):

algebraic geometry, commutative algebraPublications listed on MathSciNet, but only up to 2006. For current list, see www.math.purdue.edu/~lipman .

- [1] Hung-Jen Chiang-Hsieh and Joseph Lipman. A numerical criterion for simultaneous normalization. Duke Math. J., 133(2):347-390, 2006.
- [2] Pramathanath Sastry. Correction to: “Regular differential and equidimensional scheme-maps” [J. Algebraic Geom. 1 (1992), no. 1, 101-130; 1129841] by J. Lipman and Sastry. J. Algebraic Geom., 14(4):593-599, 2005.
- [3] Joseph Lipman, Suresh Nayak, and Pramathanath Sastry. Pseudofunctorial behavior of Cousin complexes on formal schemes. In Variance and duality for Cousin complexes on formal schemes, volume 375 of Contemp. Math., pages 3-133. Amer. Math. Soc., Providence, RI, 2005.
- [4] Joseph Lipman, Suresh Nayak, and Pramathanath Sastry. Variance and duality for Cousin complexes on formal schemes, volume 375 of Contemporary Mathematics. American Mathematical Society, Providence, RI, 2005.
- [5] Joseph Lipman and Kei-ichi Watanabe. Integrally closed ideals in two-dimensional regular local rings are multiplier ideals. Math. Res. Lett., 10(4):423-434, 2003.
- [6] Leovigildo Alonso Tarrío, Ana Jeremías López, and Joseph Lipman. Correction to the paper: “Duality and flat base change on formal schemes” [in studies in duality on noetherian formal schemes and non-noetherian ordinary schemes, 3-90, Amer. Math. Soc., Providence, RI, 1999; MR1716706 (2000h:14017)]. Proc. Amer. Math. Soc., 131(2):351-357 (electronic), 2003.
- [7] Joseph Lipman. Lectures on local cohomology and duality. In Local cohomology and its applications (Guanajuato, 1999), volume 226 of Lecture Notes in Pure and Appl. Math., pages 39-89. Dekker, New York, 2002.
- [8] Joseph Lipman. Equisingularity and simultaneous resolution of singularities. In Resolution of singularities (Obergurgl, 1997), volume 181 of Progr. Math., pages 485-505. Birkhäuser, Basel, 2000.
- [9] Joseph Lipman. Oscar Zariski 1899-1986. In Resolution of singularities (Obergurgl, 1997), volume 181 of Progr. Math., pages 1-4. Birkhäuser, Basel, 2000.
- [10] H. Hauser, J. Lipman, F. Oort, and A. Quirós, editors. Resolution of singularities, volume 181 of Progress in Mathematics. Birkhäuser Verlag, Basel, 2000. A research textbook in tribute to Oscar Zariski, Papers from the Working Week held in Obergurgl, September 7-14, 1997.
- [11] Leovigildo Alonso Tarrío, Ana Jeremías López, and Joseph Lipman. Studies in duality on Noetherian formal schemes and non-Noetherian ordinary schemes, volume 244 of Contemporary Mathematics. American Mathematical Society, Providence, RI, 1999.
- [12] Weiming Huang and Joseph Lipman. Differential invariants of embeddings of manifolds in complex spaces. In Singularities (Oberwolfach, 1996), volume 162 of Progr. Math., pages 61-92. Birkhäuser, Basel, 1998.
- [13] Leovigildo Alonso Tarrío, Ana Jeremías López, and Joseph Lipman. Local homology and cohomology on schemes. Ann. Sci. École Norm. Sup. (4), 30(1):1-39, 1997.
- [14] Steven Kleiman, Joseph Lipman, and Bernd Ulrich. The multiple-point schemes of a finite curvilinear map of codimension one. Ark. Mat., 34(2):285-326, 1996.
- [15] Oscar Zariski. Algebraic surfaces. Classics in Mathematics. Springer-Verlag, Berlin, 1995. With appendices by S. S. Abhyankar, J. Lipman and D. Mumford, Preface to the appendices by Mumford, Reprint of the second (1971) edition.
- [16] Joseph Lipman. Adjoints of ideals in regular local rings. Math. Res. Lett., 1(6):739-755, 1994. With an appendix by Steven Dale Cutkosky.
- [17] Joseph Lipman. Cohen-Macaulayness in graded algebras. Math. Res. Lett., 1(2):149-157, 1994.
- [18] Joseph Lipman. Proximity inequalities for complete ideals in two-dimensional regular local rings. In Commutative algebra: syzygies, multiplicities, and birational algebra (South Hadley, MA, 1992), volume 159 of Contemp. Math., pages 293-306. Amer. Math. Soc., Providence, RI, 1994.
- [19] Joseph Lipman. Adjoints and polars of simple complete ideals in two-dimensional regular local rings. Bull. Soc. Math. Belg. Sér. A, 45(1-2):223-244, 1993. Third Week on Algebra and Algebraic Geometry (SAGA III) (Puerto de la Cruz, 1992).
- [20] Steven Kleiman, Joseph Lipman, and Bernd Ulrich. The source double-point cycle of a finite map of codimension one. In Complex projective geometry (Trieste, 1989/Bergen, 1989), volume 179 of London Math. Soc. Lecture Note Ser., pages 199-212. Cambridge Univ. Press, Cambridge, 1992.
- [21] Joseph Lipman and Pramathanath Sastry. Regular differential and equidimensional scheme-maps. J. Algebraic Geom., 1(1):101-130, 1992.
- [22] Alex D. Gottlieb and Joseph Lipman. Group-theoretic axioms for projective geometry. Canad. J. Math., 43(1):89-107, 1991.
- [23] Joseph Lipman. On complete ideals in regular local rings. In Algebraic geometry and commutative algebra, Vol.I, pages 203-231. Kinokuniya, Tokyo, 1988.
- [24] Yih-Nan Gau. Embedded topological classification of quasi-ordinary singularities. Mem. Amer. Math. Soc., 74(388):109-129, 1988. With an appendix by Joseph Lipman.
- [25] Joseph Lipman. Topological invariants of quasi-ordinary singularities. Mem. Amer. Math. Soc., 74(388):1-107, 1988.
- [26] Piotr Blass and Jeffrey Lang. Zariski surfaces and differential equations in characteristic p>0, volume 106 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker Inc., New York, 1987. With the collaboration of David Joyce, William E. Lang, Raymond Hoobler, Joseph Lipman, Marc Levine, Thorston Ekedahl and J. Blass.
- [27] Joseph Lipman. Residues and traces of differential forms via Hochschild homology, volume 61 of Contemporary Mathematics. American Mathematical Society, Providence, RI, 1987.
- [28] Joseph Lipman and Andrew John Sommese. On blowing down projective spaces in singular varieties. J. Reine Angew. Math., 362:51-62, 1985.
- [29] Joseph Lipman. Dualizing sheaves, differentials and residues on algebraic varieties. Astérisque, (117):ii+138, 1984.
- [30] Yih Nan Gau and Joseph Lipman. Differential invariance of multiplicity. In Singularities, Part 1 (Arcata, Calif., 1981), volume 40 of Proc. Sympos. Pure Math., pages 453-456. Amer. Math. Soc., Providence, R.I., 1983.
- [31] Y.-N. Gau and J. Lipman. Differential invariance of multiplicity on analytic varieties. Invent. Math., 73(2):165-188, 1983.
- [32] Joseph Lipman. Quasi-ordinary singularities of surfaces in C3. In Singularities, Part 2 (Arcata, Calif., 1981), volume 40 of Proc. Sympos. Pure Math., pages 161-172. Amer. Math. Soc., Providence, RI, 1983.
- [33] Joseph Lipman. Equimultiplicity, reduction, and blowing up. In Commutative algebra (Fairfax, Va., 1979), volume 68 of Lecture Notes in Pure and Appl. Math., pages 111-147. Dekker, New York, 1982.
- [34] Joseph Lipman and Avinash Sathaye. Jacobian ideals and a theorem of Briançon-Skoda. Michigan Math. J., 28(2):199-222, 1981.
- [35] Joseph Lipman and Bernard Teissier. Pseudorational local rings and a theorem of Briançon-Skoda about integral closures of ideals. Michigan Math. J., 28(1):97-116, 1981.
- [36] Oscar Zariski. Collected papers. Vol. IV, volume 16 of Mathematicians of Our Time. MIT Press, Cambridge, Mass., 1979. Equisingularity on algebraic varieties, Edited and with an introduction by J. Lipman and B. Teissier.
- [37] Piotr Blass and Joseph Lipman. Remarks on adjoints and arithmetic genera of algebraic varieties. Amer. J. Math., 101(2):331-336, 1979.
- [38] Joseph Lipman. Rings with discrete divisor class group: theorem of Danilov-Samuel. Amer. J. Math., 101(1):203-211, 1979.
- [39] Joseph Lipman. Double point resolutions of deformations of rational singularities. Compositio Math., 38(1):37-42, 1979.
- [40] Glenn W. Hopkins and Joseph Lipman. An elementary theory of Grothendieck's residue symbol. C. R. Math. Rep. Acad. Sci. Canada, 1(3):169-172, 1978/79.
- [41] Joseph Lipman. Desingularization of two-dimensional schemes. Ann. Math. (2), 107(1):151-207, 1978.
- [42] Joseph Lipman. The Picard group of a scheme over an Artin ring. Inst. Hautes Études Sci. Publ. Math., (46):15-86, 1976.
- [43] Joseph Lipman. Errata: “Relative Lipschitz-saturation” (Amer. J. Math. 97 (1975), no. 3, 791-813). Amer. J. Math., 98(2):517, 1976.
- [44] Joseph Lipman. Absolute saturation of one-dimensional local rings. Amer. J. Math., 97(3):771-790, 1975.
- [45] Joseph Lipman. Relative Lipschitz-saturation. Amer. J. Math., 97(3):791-813, 1975.
- [46] Joseph Lipman. Introduction to resolution of singularities. In Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974), pages 187-230. Amer. Math. Soc., Providence, R.I., 1975.
- [47] Joseph Lipman. Unique factorization in complete local rings. In Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974), pages 531-546. Amer. Math. Soc., Providence, R.I., 1975.
- [48] Joseph Lipman. Picard schemes of formal schemes; application to rings with discrete divisor class group. In Classification of algebraic varieties and compact complex manifolds, pages 94-132. Lecture Notes in Math., Vol. 412. Springer, Berlin, 1974.
- [49] Oscar Zariski. Algebraic surfaces. Springer-Verlag, New York, supplemented edition, 1971. With appendices by S. S. Abhyankar, J. Lipman, and D. Mumford, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 61.
- [50] Joseph Lipman. Stable ideals and Arf rings. Amer. J. Math., 93:649-685, 1971.
- [51] Joseph Lipman. Rational singularities, with applications to algebraic surfaces and unique factorization. Inst. Hautes Études Sci. Publ. Math., (36):195-279, 1969.
- [52] Joseph Lipman. On the Jacobian ideal of the module of differentials. Proc. Amer. Math. Soc., 21:422-426, 1969.
- [53] Joseph Lipman. Transcendental numbers. Queen's Papers in Pure and Applied Mathematics, No. 7. Queen's University, Kingston, Ont., 1966, 1966.
- [54] Joseph Lipman. Balanced field extensions. Amer. Math. Monthly, 73:373-374, 1966.
- [55] Joseph Lipman. Free derivation modules on algebraic varieties. Amer. J. Math., 87:874-898, 1965.
- [56] Joseph Lipman. Some properties of localization and normalization. Proc. Amer. Math. Soc., 16:1120-1122, 1965.
- [57] Joe Lipman. Order in affine and projective geometry. Canad. Math. Bull., 6:37-43, 1963.
- [58] Joe Lipman. Definition of affine geometry by a group of transformations. Canad. Math. Bull., 4:265-278, 1961.
- [59] J. Lipman. A lemma on continuous functions. Canad. Math. Bull., 3:186-187, 1960.
- [60] Joe Lipman. A generalization of Ceva's theorem. Amer. Math. Monthly, 67:162-163, 1960.