Title: Logarithmic coherent sheaves
Abstract: As a variety undergoes a simple normal crossing degeneration, its coherent sheaves and their moduli spaces degenerate unpredictably. Since Gieseker, one geometric idea has proved indispensable in constructing these degenerations: study sheaves on expansions of the degenerate variety. This talk will introduce logarithmic coherent sheaves, which arrange coherent sheaves across all expansions into a single abelian category, and recover known moduli spaces, including log Quot schemes, in the expected way. The associated derived category has good properties, including a version of Serre duality, and - for a simple normal crossing degeneration - the structure sheaf of the diagonal is perfect: the categorical signature of smoothness, even though the central fibre is singular. Based on joint work with Dell, Hu, Manali Rahul, and Schimpf.
The advanced seminar begins at 4:00 pm s.t..