Geodesic
Enumerating exceptional collections of line bundles on some surfaces of general type
Documenta mathematica, Tome 20 (2015), pp. 1255-1291
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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 pg​=0 and KX2​=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.
DOI : 10.4171/dm/519
Classification : 14J29
Mots-clés : derived category, kulikov surface, burniat surface, Beauville surface, semiorthogonal decomposition, exceptional sequence, Hochschild homology 
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     author = {Stephen Coughlan},
     title = {Enumerating exceptional collections of line bundles on some surfaces of general type},
     journal = {Documenta mathematica},
     pages = {1255--1291},
     year = {2015},
     volume = {20},
     doi = {10.4171/dm/519},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/519/}
}
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Stephen Coughlan. Enumerating exceptional collections of line bundles on some surfaces of general type. Documenta mathematica, Tome 20 (2015), pp. 1255-1291. doi: 10.4171/dm/519

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