Geodesic
Enumerating exceptional collections of line bundles on some surfaces of general type
Documenta mathematica, Tome 20 (2015), pp. 1255-1291.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 14F05, 14J29
Keywords: derived category, kulikov surface, burniat surface, Beauville surface, semiorthogonal decomposition, exceptional sequence, Hochschild homology 
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     author = {Coughlan, Stephen},
     title = {Enumerating exceptional collections of line bundles on some surfaces of general type},
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Coughlan, Stephen. Enumerating exceptional collections of line bundles on some surfaces of general type. Documenta mathematica, Tome 20 (2015), pp. 1255-1291. http://geodesic.mathdoc.fr/item/DOCMA_2015__20__a5/