2011/08/25 by Yukinobu Toda, Toda, Yukinobu
Mathematics · #14N35 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14N35
paper · pdf · doi:10.48550/arxiv.1108.4992
46pages, 1figure
arxiv created 2011/08/25 · arxiv updated 2011/08/26
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.