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Relative Lefschetz Action and BPS State Counting

Shinobu Hosono·Masa-Hiko Saito·Atsushi Takahashi
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Abstract

In this paper, we propose a mathematical definition of a new ``numerical invariants" of Calabi--Yau 3-folds from stable sheaves of dimension one, which is motivated by the Gopakumar-Vafa conjecture in M-theory. Moreover, we show that for any projective morphism $f:X -> Y$ of normal projective varieties, there exists a natural $sl_2 \times sl_2$ action on the intersection cohomology group $IH(X, \Q)$ which fits into the perverse Leray spectral sequence.

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Shinobu Hosono, Masa-Hiko Saito, Atsushi Takahashi. 2001-05-17. Relative Lefschetz Action and BPS State Counting. https://doi.org/10.1155/s107379280100040x

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