Deformation of exceptional collections

Abstract

We show that in a smooth family of complete varieties, the existence of full exceptional collection on a fiber preserves for 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.

Typos corrected. Presentation of the introduction improved. One open problem modified