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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.


References [Enhancements On Off] (What's this?)

  • [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

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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

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