Minimal rational curves on 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.

Minor corrections and additions. Accepted for publication at Compositio Mathematica