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arXiv · 1206.1830

On the derived category of the classical Godeaux surface

Christian Böhning·Hans-Christian Graf von Bothmer·Pawel Sosna
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Abstract

We construct an exceptional sequence of length 11 on the classical Godeaux surface X which is the Z/5-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. 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.

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Christian Böhning, Hans-Christian Graf von Bothmer, Pawel Sosna. 2012-10-03. On the derived category of the classical Godeaux surface. https://doi.org/10.1016/j.aim.2013.04.017

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