A geometric degree formula for $A$-discriminants and Euler obstructions of toric varieties

Yutaka Matsui; Kiyoshi Takeuchi

A geometric degree formula for $A$-discriminants and Euler obstructions of toric varieties

Algebraic Geometry 2008-12-14 v5

Authors: Yutaka Matsui , Kiyoshi Takeuchi

Abstract

We give explicit formulas for the dimensions and the degrees of $A$ -discriminant varieties introduced by Gelfand-Kapranov-Zelevinsky. Our formulas can be applied also to the case where the $A$ -discriminant varieties are higher-codimensional and their degrees are described by the geometry of the configurations $A$ . Moreover combinatorial formulas for the Euler obstructions of general (not necessarily normal) toric varieties will be also given.

Keywords

A-discriminant toric varieties Euler obstruction degree formula Gelfand-Kapranov-Zelevinsky combinatorial formula

Cite

@article{arxiv.0807.3163,
  title  = {A geometric degree formula for $A$-discriminants and Euler obstructions of toric varieties},
  author = {Yutaka Matsui and Kiyoshi Takeuchi},
  journal= {arXiv preprint arXiv:0807.3163},
  year   = {2008}
}

Comments

25 pages, Chapter 4 of the previous version was separated and became a part of a new paper submitted to the arxiv, revised

A geometric degree formula for $A$-discriminants and Euler obstructions of toric varieties

Abstract

Keywords

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