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Stable Pairs on Nodal $K3$ Fibrations
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
doi:10.1093/imrn/rnx035
fatcat:h3elv5ce2faalgd5lanbzmt5my