대한수학회지 (Journal of the Korean Mathematical Society)

  • 제57권4호
  • /
  • Pages.809-823
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  • 2020
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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DEFORMATION OF LOCALLY FREE SHEAVES AND HITCHIN PAIRS OVER NODAL CURVE

  • Sun, Hao (Department of Mathematics Sun Yat-Sen University)
  • 투고 : 2019.05.08
  • 심사 : 2020.03.03
  • 발행 : 2020.07.01
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초록

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.

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참고문헌

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