Relative Lefschetz Action and BPS State Counting

Details Relative Lefschetz Action and BPS State Counting Relative Lefschetz Action and BPS State Counting

2001-05-17

arxiv.org/abs/math/0105148v2

Internat. Math. Res. Notices, (2001), No. 15, 783-816.

Mathematics

Algebraic Geometry

latex file, 25 pages, minor corrections, typos

Scientific paper

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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