Toric residue and combinatorial degree
| dc.creator | Soprounov, Ivan | |
| dc.date | 2003-09-24 | |
| dc.date | 2004-06-16 | |
| dc.date.accessioned | 2026-07-07T05:01:25Z | |
| dc.date.available | 2026-07-07T05:01:25Z | |
| dc.description | Consider an n-dimensional projective toric variety X defined by a convex lattice polytope P. David Cox introduced the toric residue map given by a collection of n+1 divisors Z_0,...,Z_n on X. In the case when the Z_i are T-invariant divisors whose sum is X\T the toric residue map is the multiplication by an integer number. We show that this number is the degree of a certain map from the boundary of the polytope P to the boundary of a simplex. This degree can be computed combinatorially. We also study radical monomial ideals I of the homogeneous coordinate ring of X. We give a necessary and sufficient condition for a homogeneous polynomial of semiample degree to belong to I in terms of geometry of toric varieties and combinatorics of fans. Both results have applications to the problem of constructing an element of residue one for semiample degrees. | |
| dc.description | 13 pages, one section added, 1 pstex figure. To appear in Trans. Amer. Math. Soc | |
| dc.identifier | https://arxiv.org/abs/math/0309409 | |
| dc.identifier | http://arxiv.org/abs/math/0309409 | |
| dc.identifier | Trans. Amer. Math. Soc., 357 (2005), no. 5, 1963--1975 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68666 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14M25, 52B20 | |
| dc.title | Toric residue and combinatorial degree | |
| dc.type | text |