Geodesic
Cycles representing the Todd class of a toric variety
Pommersheim, James1 ; Thomas, Hugh2, 3
1 Department of Mathematics, Pomona College, Claremont, California 92037
2 Fields Institute, 222 College Street, Toronto ON, M5T 3J1 Canada
3 Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3 Canada
Journal of the American Mathematical Society, Tome 17 (2004) no. 4, pp. 983-994

Voir la notice de l'article provenant de la source American Mathematical Society

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 $\mu (\sigma )$ to each rational polyhedral cone $\sigma$ in the lattice, such that for any toric variety $X$ with fan $\Sigma$ in the lattice, we have \[ \operatorname {Td}(X)=\sum _{\sigma \in \Sigma } \mu (\sigma ) [V(\sigma )].\] 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.
DOI : 10.1090/S0894-0347-04-00460-6

Pommersheim, James 1 ; Thomas, Hugh 2, 3

1 Department of Mathematics, Pomona College, Claremont, California 92037
2 Fields Institute, 222 College Street, Toronto ON, M5T 3J1 Canada
3 Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3 Canada 
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Pommersheim, James; Thomas, Hugh. Cycles representing the Todd class of a toric variety. Journal of the American Mathematical Society, Tome 17 (2004) no. 4, pp. 983-994. doi: 10.1090/S0894-0347-04-00460-6

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