On the derived category of the classical Godeaux surface
By Christian Bohning, Hans-Christian Graf von Bothmer, Pawel Sosna. 2012
57 citations recorded by the source corpus.
Abstract We construct an exceptional sequence of length 11 on the classical Godeaux surface X which is the Z / 5 Z -quotient of the Fermat quintic surface in P 3 . This is the maximal possible length of such a sequence on this surface which has Grothendieck group Z 11 ⊕ Z / 5 Z . In particular, the result answers Kuznetsov’s Nonvanishing Conjecture, which concerns Hochschild homology of an admissible subcategory, in the negative. The sequence carries a symmetry when interpreted in terms of the root lattice of the simple Lie algebra of type E 8 . We also produce explicit nonzero objects in the (right) orthogonal to the exceptional sequence.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6a12e4d46aebdcb2706cb7244a8cdf34c8fd4140
How researchers see this paper
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In Geometry and Topology
- Alexander Kuznetsov
- Alexander Polishchuk
- Emanuele Macrì
- P. Stellari
- K. Hori
- Arend Bayer
- Alexander Perry
- T. Bridgeland
In Mathematical Physics
- Alexander Polishchuk
- Alexander Kuznetsov
- Emanuele Macrì
- K. Hori
- P. Stellari
- Alexander Perry
- Arend Bayer
- T. Bridgeland
Citations in the corpus
- Semiorthogonal decompositions in algebraic geometry (2014, background): “In fact, for many surfaces of general type with pg = q = 0 (the classical Godeaux surface, the Beauville surface, the Burniat surfaces, the determinantal Barlow surface, some fake projective planes) exceptional collections of length equal to the rank of the Grothendieck group have been constructed i”
- Exceptional collections on isotropic Grassmannians (2011, background): “gth on G/P is full. The more general Nonvanishing Conjecture of [K09] stating that every exceptional collection of expected length is full turned out to be false — counterexamples were constructed in [BBS], [AO], [GS], [BBKS]. Nevertheless, we believe that the conjecture is still true for homogeneou”