Journal of the American Mathematical Society

Author(s): Irena Peeva; Bernd Sturmfels
Journal: J. Amer. Math. Soc. 11 (1998), 363-373.
MSC (1991): Primary 13D02
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Abstract: A concept of genericity is introduced for lattice ideals (and hence for ideals defining toric varieties) which ensures nicely structured homological behavior. For a generic lattice ideal we construct its minimal free resolution and we show that it is induced from the Scarf resolution of any reverse lexicographic initial ideal.

[BS]: I. Barany and H. Scarf, Matrices with identical sets of neighbors, to appear in Mathematics of Operations Research.
[BHS]: I. Barany, R. Howe, H. Scarf, The complex of maximal lattice free simplices, Mathematical Programming 66 (1994) Ser. A, 273-281. MR 95i:90045
[BSS]: I. Barany, H. Scarf, D. Shallcross, The topological structure of maximal lattice free convex bodies: the general case, Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. 920 Springer, Berlin, 1995, 244-251. MR 97a:52003
[BPS]: D. Bayer, I. Peeva, B. Sturmfels, Monomial resolutions, Manuscript, 1996.
[PS]: I. Peeva and B. Sturmfels, Syzygies of codimension $2$ lattice ideals, to appear in Mathematische Zeitschrift.
[Sta]: R. Stanley, Combinatorics and Commutative Algebra, Birkhäuser, Boston, 1983. MR 85b:05002
[Stu]: B. Sturmfels, Gröbner Bases and Convex Polytopes, AMS University Lecture Series, Vol. 8, Providence RI, 1995. MR 97b:13034

Retrieve articles in Journal of the American Mathematical Society with MSC (1991): 13D02

Irena Peeva
Affiliation: Department of Mathematics, Massachussetts Institute of Technology, Cambridge, Massachusetts 02139
Email: irena@math.mit.edu

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ISSN: 1088-6834(e) ISSN: 0894-0347(p)

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