Generic lattice ideals

Authors:
Irena Peeva and Bernd Sturmfels

Journal:
J. Amer. Math. Soc. **11** (1998), 363-373

MSC (1991):
Primary 13D02

DOI:
https://doi.org/10.1090/S0894-0347-98-00255-0

MathSciNet review:
1475887

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Abstract | References | Similar Articles | Additional Information

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 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**

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Additional Information

**Irena Peeva**

Affiliation:
Department of Mathematics, Massachussetts Institute of Technology, Cambridge, Massachusetts 02139

Email:
irena@math.mit.edu

**Bernd Sturmfels**

Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720

Email:
bernd@math.berkeley.edu

DOI:
https://doi.org/10.1090/S0894-0347-98-00255-0

Keywords:
Syzygies,
semigroup rings,
toric varieties

Received by editor(s):
April 24, 1997

Received by editor(s) in revised form:
October 23, 1997

Article copyright:
© Copyright 1998
American Mathematical Society