Cycles representing the Todd class of a toric variety

Authors:
James Pommersheim and Hugh Thomas

Journal:
J. Amer. Math. Soc. **17** (2004), 983-994

MSC (2000):
Primary 14M25; Secondary 14C17, 52B20

DOI:
https://doi.org/10.1090/S0894-0347-04-00460-6

Published electronically:
May 25, 2004

MathSciNet review:
2083474

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we describe a way to construct cycles which represent the Todd class of a toric variety. Given a lattice with an inner product, we assign a rational number to each rational polyhedral cone in the lattice, such that for any toric variety with fan in the lattice, we have

This constitutes an improved answer to an old question of Danilov.

In a similar way, beginning from the choice of a complete flag in the lattice, we obtain the cycle Todd classes constructed by Morelli.

Our construction is based on an intersection product on cycles of a simplicial toric variety developed by the second author. Important properties of the construction are established by showing a connection to the canonical representation of the Todd class of a simplicial toric variety as a product of torus-invariant divisors developed by the first author.

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Additional Information

**James Pommersheim**

Affiliation:
Department of Mathematics, Pomona College, Claremont, California 92037

Email:
jpommersheim@pomona.edu

**Hugh Thomas**

Affiliation:
Fields Institute, 222 College Street, Toronto ON, M5T 3J1 Canada

Address at time of publication:
Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3 Canada

Email:
hthomas@fields.utoronto.ca

DOI:
https://doi.org/10.1090/S0894-0347-04-00460-6

Keywords:
Toric variety,
Todd class,
polytopes,
counting lattice points

Received by editor(s):
October 25, 2003

Published electronically:
May 25, 2004

Article copyright:
© Copyright 2004
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.