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

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.

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

References in corpus (2)

• Irregularity of hypergeometric systems via slopes along coordinate subspaces
• Milnor fibers over singular toric varieties and nearby cycle sheaves