The Gromov width of generalized Bott-Samelson manifolds

Abstract

We study the Gromov width of smooth generalized Bott-Samelson varieties, a class of projective varieties constructed by Perrin in \cite{Per07} as a generalization of classical Bott-Samelson resolutions of Schubert varieties. We show that the Gromov width of such a variety equipped with a rational Kähler form is given by the symplectic area of its minimal rational curves. As a consequence, we obtain upper bounds for the Seshadri constants of these varieties with respect to ample line bundles.