List of Publications

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.
    More about the Appendix (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.
ArXiv: math.AC/030721


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


31. (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.
ArXiv : math.AC/0412466


32. 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.
ArXiv: math.AC/0412361


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


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


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


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


37. (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



38. 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.


39. (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.


Preprints submitted


40. (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),
See also arXiv math. 1409.2192 (v.2 March 2015, 61p.).

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.

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:


4. (with Joachim Yameogo) Graded Ideals in ${\sf k}[x,y]$ and partitions of diagonal lengths $T$: the hook code, (2017) 86 p.
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.