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arXiv · 1402.1540

Enumerating exceptional collections of line bundles on some surfaces of general type

Stephen Coughlan
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Abstract

We use constructions of surfaces as abelian covers to write down exceptional collections of line bundles of maximal length for every surface $X$ in certain families of surfaces of general type with $p_g=0$ and $K_X^2=3,4,5,6,8$. We also compute the algebra of derived endomorphisms for an appropriately chosen exceptional collection, and the Hochschild cohomology of the corresponding quasiphantom category. As a consequence, we see that the subcategory generated by the exceptional collection does not vary in the family of surfaces. Finally, we describe the semigroup of effective divisors on each surface, answering a question of Alexeev.

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Stephen Coughlan. 2015-11-03. Enumerating exceptional collections of line bundles on some surfaces of general type. https://arxiv.org/abs/1402.1540

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