Algebra/Number Theory seminar

Andrea Ricolfi (SISSA) will give an algebra and number theory seminar.

Title: "Virtual invariants of Quot schemes on 3-folds"

AbstractWe show that the Quot scheme of finite length quotients of a locally free sheaf on a 3-fold carries, under suitable conditions, a 0-dimensional virtual fundamental class. Using results with S. Beentjes, we solve the associated enumerative theory for Calabi-Yau 3-folds.  We present a conjectural formula in the general case, and we develop the parallel motivic theory of Quot schemes on an arbitrary 3-fold.  The results presented provide new examples of higher rank (motivic) Donaldson-Thomas invariants.