Deformation of exceptional collections

Xiaowen Hu

Published 2018-05-10Version 1

We show that in a smooth family of Fano or anti-Fano projective varieties, the existence of full exceptional collection of a fiber preserves in the fibers in a neighborhood. Then we show that the noncommutative deformations of a strong exceptional collection of vector bundles induce the same map on the second Hochschild cohomology as the canonical isomorphism induced by the derived equivalence to the corresponding endomorphism algebra.