The isomorphism problem for Schubert varieties
Algebraic Geometry
2022-05-24 v2 Combinatorics
Abstract
Schubert varieties in the full flag variety of Kac-Moody type are indexed by elements of the corresponding Weyl group. We give a practical criterion for when two such Schubert varieties (from potentially different flag varieties) are isomorphic, in terms of the Cartan matrix and reduced words for the indexing Weyl group elements. As a corollary, we show that two such Schubert varieties are isomorphic if and only if there is an isomorphism between their integral cohomology rings that preserves the Schubert basis.
Keywords
Cite
@article{arxiv.2103.08114,
title = {The isomorphism problem for Schubert varieties},
author = {Edward Richmond and William Slofstra},
journal= {arXiv preprint arXiv:2103.08114},
year = {2022}
}
Comments
23 pages, 1 figure. Ver2: Updated and combined Examples 1.5 and 1.6. Made corrections to Example 1.7