|Speaker:||Agnieszka Bodzenta (HSE)|
|Title:||Null category of morphism of relative dimension one|
|Date (JST):||Mon, Feb 09, 2015, 14:00 - 17:00|
|Place:||Seminar Room A|
For a morphism of varieties the null category is the kernel of the derived direct image functor. It is endowed with a standard t-structure. Heart of this t-structure, the category of coherent sheaves whose derived direct images vanish, has finitely many simple objects. For a morphism of surfaces the null category has another, Ringel-dual, t-structure.
In the first part, I will prove existence of the standard t-structure on a null category of a morphism of relative dimension one. I will describe properties of this t-structure with respect to composition of morphisms. I will define the Ringel dual t-structure and prove that for morphisms of smooth surfaces the null category is scheme-theoretically supported on the discrepancy divisor. In the second part I will describe the heart of Ringel dual t-structure as a category of modules over an explicit quiver with relations. This is a joint work with Alexey Bondal.