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DEFORMATION OF LOCALLY FREE SHEAVES AND HITCHIN PAIRS OVER NODAL CURVE

  • Sun, Hao (Department of Mathematics Sun Yat-Sen University)
  • Received : 2019.05.08
  • Accepted : 2020.03.03
  • Published : 2020.07.01

Abstract

In this article, we study the deformation theory of locally free sheaves and Hitchin pairs over a nodal curve. As a special case, the infinitesimal deformation of these objects gives the tangent space of the corresponding moduli spaces, which can be used to calculate the dimension of the corresponding moduli space. The deformation theory of locally free sheaves and Hitchin pairs over a nodal curve can be interpreted as the deformation theory of generalized parabolic bundles and generalized parabolic Hitchin pairs over the normalization of the nodal curve, respectively. This interpretation is given by the correspondence between locally free sheaves over a nodal curve and generalized parabolic bundles over its normalization.

Keywords

References

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