Gr\"obner theory and tropical geometry on spherical varieties
Abstract
Let be a connected reductive algebraic group. We develop a Gr\"obner theory for multiplicity-free -algebras, as well as a tropical geometry for subschemes in a spherical homogeneous space . We define the notion of a spherical tropical variety and prove a fundamental theorem of tropical geometry in this context. We also propose a definition for a spherical amoeba in . Our work partly builds on the previous work of Vogiannou on spherical tropicalization and in some ways is complementary.
Keywords
Cite
@article{arxiv.1611.01841,
title = {Gr\"obner theory and tropical geometry on spherical varieties},
author = {Kiumars Kaveh and Christopher Manon},
journal= {arXiv preprint arXiv:1611.01841},
year = {2017}
}
Comments
Some sections throughly revised. In particular, added a subsection about fan structure on spherical tropical varieties. In the spherical tropical varieties sections, previously we used a G-line bundle on G/H, we now use a very ample G-line bundle on a projective spherical embedding of G/H. Typos corrected and presentation improved in several places. 43 pages, 1 figure