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Семинар Лаборатории алгебраической геометрии и ее приложений
17 августа 2012 г. 17:00, г. Москва, ул. Вавилова, 7
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[On the derived category of the classical Godeaux surface]
Ch. Boehning
The University of Hamburg
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Аннотация:
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. If time permits, we will include some speculations on phantom categories on the Barlow surface.
Язык доклада: английский
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