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Generic lattice ideals
Author(s):
Irena
Peeva;
Bernd
Sturmfels
Journal:
J. Amer. Math. Soc.
11
(1998),
363-373.
MSC (1991):
Primary 13D02
MathSciNet review:
1475887
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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.
References:
- [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:
10.1090/S0894-0347-98-00255-0
PII:
S 0894-0347(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
Copyright of article:
Copyright
1998,
American Mathematical Society
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