Multiple cover formula of generalized DT invariants I: Parabolic stable pairs |
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Authors: | Yukinobu Toda |
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Institution: | Institute for the Physics and Mathematics of the Universe, Todai Institute for Advanced Studies (TODIAS), University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japan |
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Abstract: | 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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Keywords: | Donaldson&ndash Thomas invariants Parabolic structures |
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