Relative Lefschetz Action and BPS State Counting
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 sl2 × sl2 action on the intersection cohomology group IH(X, ) which fits into the perverse Leray spectral sequence.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.