Stable Pairs on Nodal $K3$ Fibrations

Amin Gholampour, Artan Sheshmani, Yukinobu Toda
2017 International mathematics research notices  
We study Pandharipande-Thomas's stable pair theory on K3 fibrations over curves with possibly nodal fibers. We describe stable pair invariants of the fiberwise irreducible curve classes in terms of Kawai-Yoshioka's formula for the Euler characteristics of moduli spaces of stable pairs on K3 surfaces and Noether-Lefschetz numbers of the fibration. Moreover, we investigate the relation of these invariants with the perverse (non-commutative) stable pair invariants of the K3 fibration. In the case
more » ... hat the K3 fibration is a projective Calabi-Yau threefold, by means of wall-crossing techniques, we write the stable pair invariants in terms of the generalized Donaldson-Thomas invariants of 2-dimensional Gieseker semistable sheaves supported on the fibers.
doi:10.1093/imrn/rnx035 fatcat:h3elv5ce2faalgd5lanbzmt5my