Stable pairs on nodal K3 fibrations
Abstract
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 that 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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2013
- DOI:
- 10.48550/arXiv.1308.4722
- arXiv:
- arXiv:1308.4722
- Bibcode:
- 2013arXiv1308.4722G
- Keywords:
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- Mathematics - Algebraic Geometry;
- High Energy Physics - Theory
- E-Print:
- Published version