DMM Seminar

Speaker: Artan Sheshmani (Max Planck Institute)
Title: Donaldson-Thomas invariants of 2-dimensional torsion sheaves and modular forms
Date (JST): Mon, Feb 04, 2013, 14:00 - 17:00
Place: Seminar Room B
Abstract: We study the Donaldson-Thomas invariants of the 2-dimensional stable sheaves in a smooth projective threefold. The DT invariants are defined via integrating over the virtual fundamental class when it exists. When the threefold is a K3 surface fibration we express the DT invariants of sheaves supported on the fibers in terms of the the Euler characteristics of the Hilbert scheme of points on the K3 surface and the Noether-Lefschetz numbers of the fibration. Using this we prove the modularity of the DT invariants for threefolds given as K3 fibrations as well as local P^2 which was predicted in string theory. We develop a DT-theoretic conifold transition formula through which we compute the generating series for the invariants of Hilbert scheme of points for singular surfaces. We also use our geometric techniques to compute the generating series for DT invariants of threefolds given as complete intersections such as the quintic threefold. Finally if time permits I explain furt her application of this study such as deep connections between our torsion DT invariants and higher dimensional Knot theory as well as proof of Crepant resolution conjecture on the B-model side. This is joint work with Amin Gholampour.
Remarks: Break 15:00-15:30