Wall-crossing and invariants of higher rank Joyce-Song stable pairs

Abstract

We introduce a higher rank analog of the Joyce-Song theory of stable pairs. Given a nonsingular projective Calabi-Yau threefold $X$, we define the higher rank Joyce-Song pairs given by $O_X^r(-n)\to F$ where $F$ is a pure coherent sheaf with one dimensional support, $r>1$ and $n\gg 0$ is a fixed integer. We equip the higher rank pairs with a Joyce-Song stability condition and compute their associated invariants using the wallcrossing techniques in the category of weakly semistable objects.

arXiv commentAdded "Joyce-Song" to the title. Revised version according to referee's corrections, 26 pages, Illinois. J. Math., Vol 59, 1, 55-83, (2016)