Relative Lefschetz Action and BPS State Counting
Abstract
In this paper, we propose a mathematical definition of a new ``numerical invariants" of CalabiYau 3folds from stable sheaves of dimension one, which is motivated by the GopakumarVafa conjecture in Mtheory. 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2001
 arXiv:
 arXiv:math/0105148
 Bibcode:
 2001math......5148H
 Keywords:

 Mathematics  Algebraic Geometry;
 High Energy Physics  Theory;
 14N35;
 14F05;
 81T30
 EPrint:
 latex file, 25 pages, minor corrections, typos