Algebra & Number Theory

Piecewise polynomials, Minkowski weights, and localization on toric varieties

Eric Katz and Sam Payne

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

toric variety localization tropical geometry piecewise polynomial Minkowski weight


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.

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