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

Yutaka Matsui; Kiyoshi Takeuchi

doi:10.1016/j.aim.2010.08.020

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

Yutaka Matsui, Kiyoshi Takeuchi

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

Abstract

We give explicit formulas for the dimensions and the degrees of A-discriminant varieties introduced by Gelfand, Kapranov and 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.

Original language	English
Pages (from-to)	2040-2064
Number of pages	25
Journal	Advances in Mathematics
Volume	226
Issue number	2
DOIs	https://doi.org/10.1016/j.aim.2010.08.020
Publication status	Published - 2011 Jan 30
Externally published	Yes

Keywords

Discriminants
Euler obstructions
Toric varieties

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1016/j.aim.2010.08.020

Cite this

@article{9b2d5014c50041b8acb955407bd0213c,

title = "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 and 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 = "Discriminants, Euler obstructions, Toric varieties",

author = "Yutaka Matsui and Kiyoshi Takeuchi",

year = "2011",

month = jan,

day = "30",

doi = "10.1016/j.aim.2010.08.020",

language = "English",

volume = "226",

pages = "2040--2064",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - A geometric degree formula for A-discriminants and Euler obstructions of toric varieties

AU - Matsui, Yutaka

AU - Takeuchi, Kiyoshi

PY - 2011/1/30

Y1 - 2011/1/30

N2 - We give explicit formulas for the dimensions and the degrees of A-discriminant varieties introduced by Gelfand, Kapranov and 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.

AB - We give explicit formulas for the dimensions and the degrees of A-discriminant varieties introduced by Gelfand, Kapranov and 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.

KW - Discriminants

KW - Euler obstructions

KW - Toric varieties

UR - http://www.scopus.com/inward/record.url?scp=78149500311&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78149500311&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2010.08.020

DO - 10.1016/j.aim.2010.08.020

M3 - Article

AN - SCOPUS:78149500311

VL - 226

SP - 2040

EP - 2064

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this