Grassmannian twists on the derived category via spherical functors

TL;DR

This paper constructs new derived autoequivalences for higher-dimensional Calabi-Yau varieties using spherical functors on vector bundles over Grassmannians, generalizing known twists over projective spaces.

Contribution

It introduces a new class of autoequivalences for Calabi-Yau varieties derived from Grassmannian bundles, extending the spherical twist concept.

Findings

Autoequivalences constructed for specific Calabi-Yau varieties.

Generalization of Seidel-Thomas spherical twists.

Verification of autoequivalence property for r=2 case.

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,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.