Christian Boehning

Christian Boehning (Georg-August Universität Göttingen) посетил Лабораторию в августе 2012 г.

17 августа 2012 года он выступил с докладом "On the derived category of the classical Godeaux surface" (http://arxiv.org/abs/1206.1830) на еженедельном семинаре Лаборатории.

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 P³. This is the maximal possible length of such a sequence on this surface which has Grothendieck group Z¹¹+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 E₈. 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.