On the derived category of the classical Godeaux surface
Christian Böhning (Hamburg)
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Jun 28, 2012 from 03:15 pm to 04:15 pm 
Where  Mainz, 05432 (Hilbertraum) 
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Abstract: We construct an exceptional sequence of length 11 on the classical Godeaux surface X which is the Z/5quotient 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. 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.