Grassmannian twists on the derived category via spherical functors

Abstract

We construct new examples of derived autoequivalences for a family of higher-dimensional Calabi–Yau varieties. Specifically, we take the total spaces of certain natural vector bundles over Grassmannians G r ( r , d ) of r-planes in a d-dimensional vector space, and define endofunctors of the bounded derived categories of coherent sheaves associated to these varieties. In the case r = 2, we show that these are autoequivalences using the theory of spherical functors. Our autoequivalences naturally generalize the Seidel–Thomas spherical twist for analogous bundles over projective spaces.