Lattice polygons and Green's theorem

Author:
Hal Schenck

Journal:
Proc. Amer. Math. Soc. **132** (2004), 3509-3512

MSC (2000):
Primary 14M25; Secondary 14J30, 52B35

DOI:
https://doi.org/10.1090/S0002-9939-04-07523-9

Published electronically:
May 21, 2004

MathSciNet review:
2084071

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Abstract | References | Similar Articles | Additional Information

Abstract: Associated to an -dimensional integral convex polytope is a toric variety and divisor , such that the integral points of represent . We study the free resolution of the homogeneous coordinate ring as a module over . It turns out that a simple application of Green's theorem yields good bounds for the linear syzygies of a projective toric surface. In particular, for a planar polytope , satisfies Green's condition if contains at least lattice points.

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Additional Information

**Hal Schenck**

Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843

Email:
schenck@math.tamu.edu

DOI:
https://doi.org/10.1090/S0002-9939-04-07523-9

Keywords:
Toric variety,
Green's theorem,
free resolution,
syzygy

Received by editor(s):
April 10, 2002

Received by editor(s) in revised form:
August 26, 2003

Published electronically:
May 21, 2004

Additional Notes:
The author was supported in part by NSA Grant #MDA904-03-1-0006

Communicated by:
Michael Stillman

Article copyright:
© Copyright 2004
American Mathematical Society