Minimal rational curves on generalized Bott-Samelson varieties

TL;DR

This paper studies minimal rational curves on Schubert varieties and their resolutions, providing descriptions of minimal families on small resolutions, with a focus on minuscule cases, advancing understanding of their geometric structures.

Contribution

It introduces a detailed analysis of minimal rational curves on Bott-Samelson varieties and their generalizations, especially in minuscule cases, expanding geometric insights.

Findings

Descriptions of minimal rational curves on small resolutions of minuscule Schubert varieties.

Characterization of minimal families on Bott-Samelson desingularizations.

Extension of known results to generalized Bott-Samelson varieties.

Abstract

We investigate families of minimal rational curves on Schubert varieties, their Bott-Samelson desingularizations, and their generalizations constructed by Nicolas Perrin in the minuscule case. In particular, we describe the minimal families on small resolutions of minuscule Schubert varieties.