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Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 

 

Generic lattice ideals


Authors: Irena Peeva and 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 [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] Imre Bárány, Roger Howe, and Herbert E. Scarf, The complex of maximal lattice free simplices, Math. Programming 66 (1994), no. 3, Ser. A, 273–281. MR 1297067, 10.1007/BF01581150
  • [BSS] I. Bárány, H. E. Scarf, and D. Shallcross, The topological structure of maximal lattice free convex bodies: the general case, Integer programming and combinatorial optimization (Copenhagen, 1995), Lecture Notes in Comput. Sci., vol. 920, Springer, Berlin, 1995, pp. 244–251. MR 1367985, 10.1007/3-540-59408-6_55
  • [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] Richard P. Stanley, Combinatorics and commutative algebra, Progress in Mathematics, vol. 41, Birkhäuser Boston, Inc., Boston, MA, 1983. MR 725505
  • [Stu] Bernd Sturmfels, Gröbner bases and convex polytopes, University Lecture Series, vol. 8, American Mathematical Society, Providence, RI, 1996. MR 1363949

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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