Algebra & Number Theory

Piecewise polynomials, Minkowski weights, and localization on toric varieties

Eric Katz and Sam Payne

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Abstract

We use localization to describe the restriction map from equivariant Chow cohomology to ordinary Chow cohomology for complete toric varieties in terms of piecewise polynomial functions and Minkowski weights. We compute examples showing that this map is not surjective in general, and that its kernel is not always generated in degree one. We prove a localization formula for mixed volumes of lattice polytopes and, more generally, a Bott residue formula for toric vector bundles.

Article information

Source
Algebra Number Theory, Volume 2, Number 2 (2008), 135-155.

Dates
Received: 2 April 2007
Revised: 22 October 2007
Accepted: 20 November 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513797227

Digital Object Identifier
doi:10.2140/ant.2008.2.135

Mathematical Reviews number (MathSciNet)
MR2377366

Zentralblatt MATH identifier
1158.14042

Subjects
Primary: 14M25: Toric varieties, Newton polyhedra [See also 52B20]
Secondary: 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15] 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]

Keywords
toric variety localization tropical geometry piecewise polynomial Minkowski weight

Citation

Katz, Eric; Payne, Sam. Piecewise polynomials, Minkowski weights, and localization on toric varieties. Algebra Number Theory 2 (2008), no. 2, 135--155. doi:10.2140/ant.2008.2.135. https://projecteuclid.org/euclid.ant/1513797227


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