|Speaker:||Ragnar-Olaf Buchweitz (University of Toronto)|
|Title:||The Annihilator of the Derived Singularity Category|
|Date (JST):||Tue, Aug 17, 2010, 13:30 - 15:00|
|Place:||Seminar Room A|
Given a space with Gorenstein singularities, one may attach to it its derived singularity category a la Orlov, the quotient of the derived category of all coherent sheaves on the space modulo the subcategory of perfect complexes. In the hypersurface case it is equivalent to the (stable) category of matrix factorizations.
In general, if the singularities are isolated, this is a Hom-finite category with Serre duality, and it is natural to ask what universally annihilates the Hom-sets in this category. We give, in joint work with Flenner, a lower bound in terms of a stable Atiyah-Chern character as well as through the characteristic class of the space, the map from ordinary top degree differential forms to the regular differentials that are the sections of the canonical bundle.
We show that this bound is sometimes, but not always, sharp.
These results raise some interesting questions: it suggests that there are special singularities, for which the stable Atiyah-Chern character "misses" information, while on the other hand these results give tighter bounds for matrix factorizations than one is lead to expect from work by Dyckerhoff, Takahashi and others.