Multiple cover formula of generalized DT invariants I: parabolic stable pairs

Details Multiple cover formula of generalized DT invariants I: parabolic stable pairs Multiple cover formula of generalized DT invariants I: parabolic stable pairs

2011-08-25

arxiv.org/abs/1108.4992v1

Mathematics

Algebraic Geometry

46pages, 1figure

Scientific paper

In this paper, we introduce the notion of parabolic stable pairs on Calabi-Yau 3-folds and invariants counting them. By applying the wall-crossing formula developed by Joyce-Song, Kontsevich-Soibelman, we see that they are related to generalized Donaldson-Thomas invariants counting one dimensional semistable sheaves on Calabi-Yau 3-folds. Consequently, the conjectural multiple cover formula of generalized DT invariants is shown to be equivalent to a certain product expansion formula of the generating series of parabolic stable pair invariants. The application of this result to the multiple cover formula will be pursued in the subsequent paper.

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