Lower Bounds in Real Algebraic Geometry and Orientability of Real Toric Varieties

被引：0

作者：

Soprunova, Evgenia ^{[1
]}

Sottile, Frank ^{[2
]}

机构：

[1] Kent State Univ, Dept Math, Kent, OH 44242 USA

[2] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2013年 / 50卷 / 02期

关键词：

Real toric variety; Polynomial system; Order polytope; SCHUBERT CALCULUS; POLYTOPES;

D O I：

10.1007/s00454-013-9498-9

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The real solutions to a system of sparse polynomial equations may be realized as a fiber of a projection map from a toric variety. When the toric variety is orientable, the degree of this map is a lower bound for the number of real solutions to the system of equations. We strengthen previous work by characterizing when the toric variety is orientable. This is based on work of Nakayama and Nishimura, who characterized the orientability of smooth real toric varieties.

引用

页码：509 / 519

页数：11

共 23 条

[1]

[Anonymous], 1993, Annals of Mathematics Studies, 131. The William H. Roever Lectures in Geometry

[2] Some Lower Bounds in the B. and M. Shapiro Conjecture for Flag Varieties [J].