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Moduli spaces of stable pairs

Yinbang Lin YMSC, Tsinghua University

mathscidoc:1904.01001

Pacific Journal of Mathematics, 294, (1), 123-158, 2018
We construct a moduli space of stable pairs over a smooth projective variety, parametrizing morphisms from a fixed coherent sheaf to a varying sheaf of fixed topological type, subject to a stability condition. This generalizes the notion used by Pandharipande and Thomas, following Le Potier, where the fixed sheaf is the structure sheaf of the variety. We then describe the relevant deformation and obstruction theories. We also show the existence of the virtual fundamental class in special cases.
moduli space, stable pair, deformation, obstruction, virtual fundamental class
[ Download ] [ 2019-04-10 15:14:41 uploaded by yinbang ] [ 1640 downloads ] [ 0 comments ] 
@inproceedings{yinbang2018moduli,
  title={Moduli spaces of stable pairs},
  author={Yinbang Lin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190410151442011333226},
  booktitle={Pacific Journal of Mathematics},
  volume={294},
  number={1},
  pages={123-158},
  year={2018},
}
Yinbang Lin. Moduli spaces of stable pairs. 2018. Vol. 294. In Pacific Journal of Mathematics. pp.123-158. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190410151442011333226.
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