On derived categories of nonminimal Enriques surfaces

Abstract

By Orlov's formula, the derived category of blow up must contain the original variety as a semiorthogonal component. This arises an interesting question: does there exist a variety $X$ such that $D^{\mathsf{b}}(X)$ does not admit an exceptional collection of maximal length, but $D^{\mathsf{b}}({\mathrm{Bl}}_{x}X)$ admits such a collection? We give such an example where $X$ is a minimal Enriques surface.

9 pages

References in corpus (1)

• Exceptional collections on Dolgachev surfaces associated with degenerations