The Gromov width of Bott-Samelson varieties

Abstract

We prove that the Gromov width of any Bott-Samelson variety birational to a Schubert variety and equipped with a rational K\"ahler form equals the symplectic area of a minimal curve. From this, we derive an estimate for the Seshadri constants of ample line bundles on Bott-Samelson varieties.