Chern-Mather classes of toric varieties
Algebraic Geometry
2016-04-12 v1
Abstract
The purpose of this short note is to prove a formula for the Chern-Mather classes of a toric variety in terms of its orbits and the local Euler obstructions at general points of each orbit (Theorem 2). We use the general definition of the Chern-Schwartz-MacPherson classes (see [7]) and their special expression in case of a toric variety (see [2]). As a corollary, we obtain a formula by Matsui-Takeuchi [8, Corollary 1.6]. Alternatively, one could deduce the formula of Theorem 2 from the Matsui-Takeuchi formula, by using our general result [11, Theoreme 3] for the degree of the polar varieties in terms of the Chern-Mather classes.
Keywords
Cite
@article{arxiv.1604.02845,
title = {Chern-Mather classes of toric varieties},
author = {Ragni Piene},
journal= {arXiv preprint arXiv:1604.02845},
year = {2016}
}