Combinatorial Construction of Toric Residues

Amit Khetan; Ivan Soprunov

doi:10.5802/aif.2106

Combinatorial Construction of Toric Residues

Amit Khetan, Ivan Soprunov

University of Massachusetts

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we investigate the problem of finding an explicit element whose toric residue is equal to one. Such an element is shown to exist if and only if the associated polytopes are essential. We reduce the problem to finding a collection of partitions of the lattice points in the polytopes satisfying a certain combinatorial property. We use this description to solve the problem when n=2 and for any n when the polytopes of the divisors share a complete flag of faces. The latter generalizes earlier results when the divisors were all ample

Original language	American English
Journal	Annales de l'institut Fourier
Volume	55
DOIs	https://doi.org/10.5802/aif.2106
State	Published - Jan 1 2005

Keywords

Toric varieties
toric residues
semi-ample degrees
facet colorings
combinatorial degree

Disciplines

Mathematics

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10.5802/aif.2106License: CC BY

Combinatorial Construction of Toric ResiduesFinal published version, 2.1 MBLicense: CC BY

Cite this

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title = "Combinatorial Construction of Toric Residues",

abstract = " In this paper we investigate the problem of finding an explicit element whose toric residue is equal to one. Such an element is shown to exist if and only if the associated polytopes are essential. We reduce the problem to finding a collection of partitions of the lattice points in the polytopes satisfying a certain combinatorial property. We use this description to solve the problem when n=2 and for any n when the polytopes of the divisors share a complete flag of faces. The latter generalizes earlier results when the divisors were all ample",

keywords = "Toric varieties, toric residues, semi-ample degrees, facet colorings, combinatorial degree",

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AU - Soprunov, Ivan

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N2 - In this paper we investigate the problem of finding an explicit element whose toric residue is equal to one. Such an element is shown to exist if and only if the associated polytopes are essential. We reduce the problem to finding a collection of partitions of the lattice points in the polytopes satisfying a certain combinatorial property. We use this description to solve the problem when n=2 and for any n when the polytopes of the divisors share a complete flag of faces. The latter generalizes earlier results when the divisors were all ample

AB - In this paper we investigate the problem of finding an explicit element whose toric residue is equal to one. Such an element is shown to exist if and only if the associated polytopes are essential. We reduce the problem to finding a collection of partitions of the lattice points in the polytopes satisfying a certain combinatorial property. We use this description to solve the problem when n=2 and for any n when the polytopes of the divisors share a complete flag of faces. The latter generalizes earlier results when the divisors were all ample

KW - Toric varieties

KW - toric residues

KW - semi-ample degrees

KW - facet colorings

KW - combinatorial degree

UR - https://engagedscholarship.csuohio.edu/scimath_facpub/271

U2 - 10.5802/aif.2106

DO - 10.5802/aif.2106

M3 - Article

VL - 55

JO - Annales de l'institut Fourier

JF - Annales de l'institut Fourier

ER -

Combinatorial Construction of Toric Residues

Abstract

Keywords

Disciplines

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