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Oberseminar WiSe 2010/11 Zusammenfassung des Vortrags von Malte Wandel

Moduli spaces of stable pairs in Donaldson-Thomas theory

Studying CY 3-folds, one may ask how many curves of fixed type (fix for example the euler characteristic and the cycle class) one can find on such a CY. The answer can be given by different invariants such as the Gromov-Witten invariants. They can be defined as the integral of a virtual class over the moduli space of curves of the specific type. These moduli problems are not compact and there are different types of compactification. The approach by Pandharipande and Thomas leads to the notion of stable pairs. I will describe the construction of a coarse moduli space for these stable pairs and will give some account on a relation to the work of Joseph Le Potier about coherent systems.