GT Seminar with Nick Kuhn (University of Oslo)

Abstract: In the paper "Floer homology and algebraic geometry", Donaldson raised the question of constructing an algebraic theory for moduli spaces of vector bundles on algebraic surfaces which are singular along a nodal divisor. A succesful candidate for such a theory would enable one to compute sheaf-theoretic invariants of a smoothing of the singular surface in terms of relative invariants of its normalization, similar to the degeneration formulas in Gromov-Witten or Donaldson-Thomas theory. 

I will present work in progress on a good theory of sheaves on degenerations that works when the surface degenerates together with a fibration to a curve. This opens the door for many interesting computations - for example, one can recover and strengthen results about the geometry of moduli spaces on elliptic surfaces.

See upcoming seminars in our seminar series on Geometry and Topology (GT).