List of Publications

Ph.D. thesis Families of ideals in a power series ring in two variables, (Arthur Mattuck, advisor), M.I.T., 1970.

Articles and Books that have appeared:

1. Punctual Hilbert Schemes, BAMS 78 (1972), 810-823 (MR 46 #7235).

2. Reducibility of the family of 0-dimensional schemes on a variety, Inventiones Math. 15 (1972), 72-77 (MR 46 #170).

3. Number of generic singularities, Rice University Studies 59, Part 1 (1972), 49-52 (MR 49 #10693).

4. An algebraic fibre bundle over $P^1$ that is not a vector bundle, Topology 12 (1973) (MR 49 #5009)

5. Memoir, AMS. Punctual Hilbert schemes. Mem. Amer. Math. Soc. 10 (1977), no. 188, viii+112 pp.

6. (with Jacques Emsalem) Some zero-dimensional generic singularities: finite algebras having small tangent spaces, Compositio Math. 36 (1978), 145-188 (MR 81c #14004).

7. (with Alan Altman and Steven Kleiman) Irreducibility of the compactified Jacobian , pp. 1-12 in Real and Complex Singularities, Oslo 1976, P. Holm, editor, Sijthoff & Noordhoff, Alphen aan den Rign, Netherlands, 1978 (MR 58 #16650).

8. (with Joel Briancon) Dimension of the punctual Hilbert scheme, Journal of Algebra 55 (1978), no. 2, 536--544. (MR0523473 (80g:14013)).

9. Deformations of zero-dimensional complete intersections, after M. Granger, T. Gaffney, with appendix: Global Hilbert Scheme $Hilb^QP^r$ after Gotzmann, pp. 92-105 in Proceedings of the Week of Algebraic Geoemtry, Bucharest, 1980, L. Badescu and H. Kurke, editors, Teubnertexte #40, B.G. Teubner, Leipzig, 1981 (MR 84j:14012).

10. Deforming complete intersection Artin algebras., pp. 593-608 in Singularities, PSPM #40, part 1, American Math Society, Providence, RI, 1983.

11. Compressed algebras: Artin algebras having given socle degrees and maximal length, Trans. AMS 285 (1984),337-378.

12. Compressed algebras and components of the punctual Hilbert scheme, pp.146-185 in Algebraic Geometry, Sitges 1983, Lecture Notes in Math. vol 1124, Springer-Verlag 1985.

13. Tangent cone of a Gorenstein singularity, in Proceedings of the conference on Algebraic Geometry, Berlin 1985, H.Kurke and M. Roczen, eds., Teubnertexte zur math. vol. 92, Teubner, Leipzig, 1986, pp. 163-176.

14. (with Joan Elias) The Hilbert function of a Cohen-Macaulay local algebra: extremal Gorenstein algebras, J. Algebra 110 (1987), 344-356.

15. Hilbert scheme of points: Overview of last ten years, in Algebraic Geometry, Bowdoin 1985, S. Bloch, editor, PSPM #46 Part 2, Amer. Math. Soc.,Providence, 1987, pp. 297-320

16. The Hilbert function of a Gorenstein Artin algebra, p.348- 364 in Commutative Algebra, Proceedings of a Microprogram held June 15-July 2,1987 at MSRI, M. Hochster, C. Hunecke, J.D. Sally, Editors, Springer-Verlag, New York, 1989.

17. (with David Bernstein) A nonunimodal graded Gorenstein Artin algebra in codimension five, Comm. in Algebra 20(8), (1992), 2323-2336.

18. Memoir, AMS.  Associated graded algebra of a Gorenstein Artin algebra, 117 p.,AMS Memoir Vol. 107 #524 (1994).

19. (with Jacques Emsalem), Inverse system of a symbolic power I.   J. Algebra, 174, (1995), 1080-1090

20. Inverse system of a symbolic power, II: the Waring problem for forms, J of Algebra, 174, (1995), 1091-1110.

21. Inverse system of a symbolic power III: thin algebras and fat points, Compositio Math. 108, (1997), 319-356.

22. Gorenstein Artin algebras, additive decompositions of forms and the punctual Hilbert scheme, in Commutative Algebra, Algebraic Geometry, and Computational Methods [Proceedings of Hanoi Conference in Commutative Algebra (1996)], D. Eisenbud, ed., Springer-Verlag (1999), 53--96. For downloadable dvi file: Gor-Art.tex.dvi

23. Book (With Vassil Kanev)
Power Sums, Gorenstein Algebras, and Determinantal Loci, 345+xxvii p., Springer Lecture Notes in Mathematics #1721, December, 1999. More about the book

24. (With Steven L. Kleiman) The Gotzmann Theorems and the Hilbert Scheme, Appendix C to above book, 23p.
(The Appendix is separately listed on the title page of book)

25. (With Clare D'Cruz), High order vanishing ideals at $n+3$ points of $\mathbf P^n$, in Commutative algebra, homological algebra and representation theory (Catania/Genoa/Rome, 1998). J. Pure Appl. Algebra 152 (2000), no. 1-3, 75--82.

26. (With Young Hyun Cho), Hilbert functions of level algebras, J. Algebra 241 (2001), 745-758. For downloadable dvi file of related preprint: Hilblev.dvi;

27. Dr. Ruth I. Michler's Research, p. 1-7 in Topics in Algebraic and Noncommutative Geometry: Proceedings in memory of Ruth Michler'', C. Melles, J. Brasselet, and G. Kennedy, editors, AMS Contemporary Mathematics series, # 324, 2003.

28. (With Joachim Yameogo) The family G_T of graded Artinian quotients G_T of k[x,y] of given Hilbert function, Communications in Algebra, Vol. 31 \# 8, 3863--3916 (2003). http://dx.doi.org/10.1081/AGB-120022447

29. Ancestor ideals of vector spaces of forms, and level algebras, J. Algebra, 272 (2004), 530--580.
30. ArXiv: math.AC/030721

31. Betti strata of height two ideals, J. Algebra 285 (2005) no. 2, 835--855.
32. ArXiv : math.AC/0407364

33. (With Hema Srinivasan) Some Gorenstein Artin algebras of embedding dimension four: Components of $\PGOR (H)$ for $H=(1,4,7,\ldots ,1)$, Journal of Pure and Applied Algebra 201 (2005) # 1-3. 62--96.
34. ArXiv : math.AC/0412466

35. Hilbert functions of Gorenstein algebras associated to a pencil of forms, p. 273-286 in Proceedings of the Conference on Projective Varieties with Unexpected Properties, C. Ciliberto, A. Geramita, B. Harbourne, R. Mir\'o-Roig, K. Ranestad, editors (de Gruyter) (2005) ISBN-10:3-11-018160-6.
36. ArXiv: math.AC/0412361

37. (with Roberta Basili) Pairs of commuting nilpotent matrices, and Hilbert function, J. Algebra 320 # 3 (2008), 1235-1254. ArXiv math.AC: 0709.2304.

38. (with Mats Boij) Reducible family of height three level algebras,J. Algebra 321 (2009), 86--104. ArXiv: math.AC/0707.2148.

39. (with Roberta Basili and Leila Khatami), Commuting nilpotent matrices and Artinian algebras, J. Commutative Algebra (2) #3 (2010), p. 295--325.

40. (With Young Hyun Cho), Inverse systems of zero-dimensional schemes in $\mathbb P^n$, J. Algebra 366 (2012), 42-77.
41. ArXiv 1107.0094

42. (with Leila Khatami), Bound on the Jordan type of a generic nilpotent matrix commuting with a given matrix, J. of Algebraic Combinatorics, 38 (2013) #4, 947-972. ArXiv 1204.4635

43. Strata of families of vector spaces of forms in R={k}[x,y], and of rational curves in $\mathbb P^{k}$,}, Bull. Braz. Math. Soc. (N.S.) 45 (2014), no. 4, 711-725.

44. (with David Cox), Strata of families of vector spaces of forms in $R={k}[x,y]$, and of rational curves in $\mathbb P^{k}$, Bull. Braz. Math. Soc. (N.S.) 45 (2014), no. 4, 711-725.

45. Preprints submitted

46. (with Leila Khatami, Bart Van Steirteghem, and Rui Zhao), Nilpotent matrices having a given Jordan type as maximum commuting nilpotent orbit, (revised July 2016, 43 p),

Reports (not refereed)
1. (with Jacques Emsalem) R$\'e$seaux de coniques et alg$`e$bres de longueur 7 associ$\'e$es (Nets of conics and length 7 algebras associated to them), 49p., U. of Paris VII, (1977).

2. Vanishing ideals at multiple points of $P^r$, p. 109-113, in Commutative Algebra, Extended abstracts of an International Conference at Vechta, 1994, W. Bruns, editor (1994).(BD 13).

3. (With V. Kanev), The length of a homogeneous form, determinantal loci of catalecticants and Gorenstein algebras, preprint, 150 p.. 1996.

4. An early version of the book [23], this was circulated, and led to work by several other groups. This version was a rather more specialized monograph preprint than the actual book [23]. Since this preprint was circulated and referenced in some articles by others, we listed in Appendix E of [23] which sections of the book replace which sections of this preprint.

Preprints or articles in preparation:

5. (with Joachim Yameogo) Graded Ideals in ${\sf k}[x,y]$ and partitions of diagonal lengths $T$: the hook code, (2017) 86 p.
6. Substantial revision and rewriting based originally on a preprint with similar title from 1994 of 48p. The 1994 preprint had combinatorial results related to [28]. The current version has further combinatorial and also geometric results.

• (with Pedro Marques), Symmetric Decomposition of the Associated Graded Algebra of an Artinian Gorenstein algebra, (2017) 84p.

1. (with M. Boij) Duality for central simple modules of Artinian Gorenstein algebras.

2. (with Franco Ghione, Gianni Sacchiero), Restricted Tangent Bundles of Rational Curves in $\mathbb P^r$, (revision of older preprint in progress)

3. Consecutive genera for irreducible Arithmetically Cohen-Macaulay Space Curves.

4. Annotated publication list (Includes brief descriptions, and some context)

Ph.D. students' articles related to dissertation