English

On the Classification of Schubert Varieties in Partial Flag Varieties

Combinatorics 2025-11-25 v3 Algebraic Geometry Representation Theory

Abstract

We generalize the classification of isomorphism classes of Schubert varieties in complete flag varieties G/B to a class of partial flag varieties G/P. In particular, we classify all Schubert varieties in G/P where P is a minimal parabolic subgroup and all Schubert surfaces. We also obtain several pairs of isomorphisms of Schubert varieties from folding the root system. This allows us to find an upper bound of the cardinality of isomorphism classes of Schubert three-folds.

Keywords

Cite

@article{arxiv.2412.02150,
  title  = {On the Classification of Schubert Varieties in Partial Flag Varieties},
  author = {Yanjun Chen},
  journal= {arXiv preprint arXiv:2412.02150},
  year   = {2025}
}