KIAS winter school on virtual enumerative geometry
Virtual counts on surfaces(Lecture 1)
SPEAKER | Martijn Kool
DATE | January 6(Tue), 2015
TIME | 16:30
PLACE | 1114 International conference room, KIAS
ABSTRACT | Abstract: This series of lectures is divided in three parts. In part 1 I review a sheaf theory of R. Pandharipande and R. P. Thomas known as stable pair theory. Stable pair invariants are closely related to both Gromov-Witten and Donaldson-Thomas invariants. In part 2 we study virtual cycles on Hilbert schemes of curves with points on surfaces. In the absence of points these give rise to the Poincare invariants of M. Durr, A. Kabanov and Ch. Okonek. Poincare invariants are an algebraic version of Seiberg-Witten invariants. In part 3 we relate the virtual cycles of part 1 and part 2 for the total space of the canonical bundle over a surface. We apply the MNOP correspondence in this setting to obtain characterizations of Severi degrees and Seiberg-Witten invariants.