Deformation of exceptional collections

• DOI: 10.48550/arxiv.1805.04050
• Publication Date: 2018-01-01
• Authors: Hu, Xiaowen
• Keywords: Mathematics - Algebraic Geometry; Mathematics - K-Theory and Homology; FOS: Mathematics; K-Theory and Homology (math.KT); 0101 mathematics; 01 natural sciences; Algebraic Geometry (math.AG)

Typos corrected. Presentation of the introduction improved. One open problem modified<br/>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.<br/>