On the derived category of the classical Godeaux surface
Algebraic Geometry
2015-03-11 v2
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.
Keywords
Cite
@article{arxiv.1206.1830,
title = {On the derived category of the classical Godeaux surface},
author = {Christian Böhning and Hans-Christian Graf von Bothmer and Pawel Sosna},
journal= {arXiv preprint arXiv:1206.1830},
year = {2015}
}
Comments
33 pages, 1 figure; version 2: apart from small changes, section 10 on the derived endomorphism algebra of the sequence added