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Institute for the Physics and Mathematics of the UniverseWPI

IPMU Seminar

Date: August 4, Monday, 2008, 13:00 - 14:30 & 15:30 - 17:00
Place: Seminar Room at IPMU Prefab. B, Kashiwa Campus of the University of Tokyo
Speaker: Nagao Kentaro (Kyoto University)
Title: Counting invariants of perverse coherent systems on CY 3-folds and their wall-crossings
Abstract: A perverse coherent system on a CY 3-fold is a pair of perverse coherent sheaf on the CY 3-fold and a morphism to it from the structure sheaf. We intruduce moduli spaces of perverse coherent systems and counting invariants of them. In order to construct a moduli space we should choose a parameter of stability. We show that Donaldson-Thomas theory and Pandharipande-Thomas theory can be recovered at specific parameters. We also establish wall-crossing formulas for the generating functions of counting invariants of perverse coherent systems. As applications, we provide some formulas on DT invariants and PT invariants.