Deformation of Locally Free Sheaves and Hitchin Pairs over Nodal curve
J. Korean Math. Soc. 2020 Vol. 57, No. 4, 809-823
https://doi.org/10.4134/JKMS.j190334
Published online July 1, 2020
Hao Sun
Sun Yat-Sen University
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 : Hitchin pair, nodal curve, generalized parabolic bundle, generalized parabolic Hitchin pair
MSC numbers : Primary 13D10, 14B12
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