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.

arXiv commentTypos corrected. Presentation of the introduction improved. One open problem modified

References in corpus (8)

• Base change for semiorthogonal decompositions
• Geometry and analytic theory of Frobenius manifolds
• Determinantal Barlow surfaces and phantom categories
• Height of exceptional collections and Hochschild cohomology of quasiphantom categories
• Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields
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• Does full imply faithful?
• Non-split Brauer-Severi varieties do not admit full exceptional collections

Cited by in corpus (2)

• Towards a specialization map modulo semi-orthogonal decompositions
• Cyclic stratum of Frobenius manifolds, Borel-Laplace $(\mathbf{\alpha },\mathbf{\beta })$-multitransforms, and integral representations of solutions of Quantum Differential Equations