Exceptional collections of line bundles on the Beauville surface

Abstract

We construct quasi-phantom admissible subcategories in the derived category of coherent sheaves on the Beauville surface $S$. These quasi-phantoms subcategories appear as right orthogonals to subcategories generated by exceptional collections of maximal possible length 4 on $S$. We prove that there are exactly 6 exceptional collections consisting of line bundles (up to a twist) and these collections are spires of two helices.

Revised version, accepted to Advances in Mathematics

References in corpus (7)

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• On the derived category of the classical Godeaux surface
• Derived categories of Burniat surfaces and exceptional collections
• Height of exceptional collections and Hochschild cohomology of quasiphantom categories
• Some new surfaces with $p_g=q=0$
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Cited by in corpus (20)

• Semiorthogonal decompositions in algebraic geometry
• Geometric Phantom Categories
• Exceptional collections on isotropic Grassmannians
• Derived categories of Burniat surfaces and exceptional collections
• Height of exceptional collections and Hochschild cohomology of quasiphantom categories
• Exceptional collections, and the Neron-Severi lattice for surfaces
• Nonexistence of semiorthogonal decompositions and sections of the canonical bundle
• Cycles, derived categories, and rationality
• Exceptional collections on Dolgachev surfaces associated with degenerations
• Quasiphantom categories on a family of surfaces isogenous to a higher product
• Equivalence of K3 surfaces from Verra threefolds
• Exceptional collection of objects on some fake projective planes
• Classification of full exceptional collections on smooth toric Fano varieties with Picard rank two
• Fano visitors, Fano dimension and orbifold Fano hosts
• Categorical characterization of quadrics
• Weil transfer of noncommutative motives
• Homology of some surfaces with $p_g=q=0$ isogenous to a product
• On derived categories of nonminimal Enriques surfaces
• Torsion birational motives of surfaces and unramified cohomology
• Non-commutative Toric Varieties