Computing toric degenerations of flag varieties
Abstract
We compute toric degenerations arising from the tropicalization of the full flag varieties $\mathcal{F}\ell_4$ and $\mathcal{F}\ell_5$ embedded in a product of Grassmannians. For $\mathcal{F}\ell_4$ and $\mathcal{F}\ell_5$ we compare toric degenerations arising from string polytopes and the FFLV polytope with those obtained from the tropicalization of the flag varieties. We also present a general procedure to find toric degenerations in the cases where the initial ideal arising from a cone of the tropicalization of a variety is not prime.
 Publication:

arXiv eprints
 Pub Date:
 February 2017
 arXiv:
 arXiv:1702.05480
 Bibcode:
 2017arXiv170205480B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Commutative Algebra;
 Mathematics  Combinatorics;
 Mathematics  Representation Theory;
 14M25;
 14D06;
 52B20
 EPrint:
 35 pages, 6 figures