Cycles representing the Todd class of a toric variety
| dc.creator | Pommersheim, James | |
| dc.creator | Thomas, Hugh | |
| dc.date | 2003-10-03 | |
| dc.date | 2004-05-02 | |
| dc.date.accessioned | 2026-07-07T05:01:35Z | |
| dc.date.available | 2026-07-07T05:01:35Z | |
| dc.description | 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 m(s) to each rational polyhedral cone s in the lattice, such that for any toric variety X with fan S, the Todd class of X is the sum over all cones s in S of m(s)[V(s)]. This constitutes an improved answer to an old question of Danilov. In a similar way, beginning with 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-named 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-named author. | |
| dc.description | 13 pages; version to appear in Journal of the AMS; minor modifications throughout, corrections to proof of theorem 2; LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0310036 | |
| dc.identifier | http://arxiv.org/abs/math/0310036 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68731 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14M25; 14C17 | |
| dc.title | Cycles representing the Todd class of a toric variety | |
| dc.type | text |