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Stable pairs on local k3 surfaces

Yukinobu Toda Mathematics of the Universe University of Tokyo

Differential Geometry mathscidoc:1609.10287

Journal of Differential Geometry, 92, (2), 285-371, 2012
We prove a formula which relates Euler characteristic of moduli spaces of stable pairs on local K3 surfaces to counting invariants of semistable sheaves on them. Our formula generalizes KawaiYoshioka’s formula for stable pairs with irreducible curve classes to arbitrary curve classes. We also propose a conjectural multiple cover formula of sheaf counting invariants which, combined with our main result, leads to an Euler characteristic version of KatzKlemm-Vafa conjecture for stable pairs.
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@inproceedings{yukinobu2012stable,
  title={STABLE PAIRS ON LOCAL K3 SURFACES },
  author={Yukinobu Toda},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914072231442352949},
  booktitle={Journal of Differential Geometry},
  volume={92},
  number={2},
  pages={285-371},
  year={2012},
}
Yukinobu Toda. STABLE PAIRS ON LOCAL K3 SURFACES . 2012. Vol. 92. In Journal of Differential Geometry. pp.285-371. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914072231442352949.
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