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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 (9)
참고문헌 신청
U. Bhosle / 1992 / Generalised parabolic bundles and applications to torsionfree sheaves on nodal curves / Ark. Mat 30(2):187~215
U. Bhosle / 2014 / Generalized parabolic Hitchin pairs / J. Lond. Math. Soc 89(1):1~23
I. Biswas / 1994 / An innitesimal study of the moduli of Hitchin pairs / J. London Math. Soc 49(2):219~231
O. Garca-Prada / 2007 / Betti numbers of the moduli space of rank 3 parabolic Higgs bundles / Mem. Amer. Math. Soc. 187(879):1090
A. Lo Giudice / 2016 / A compactication of the moduli space of principal Higgs bundles over singular curves / J. Geom. Phys 110:328~342
U. Bhosle / 2014 / Generalized parabolic Hitchin pairs / J. Lond. Math. Soc 89(1):1~23
I. Biswas / 1994 / An innitesimal study of the moduli of Hitchin pairs / J. London Math. Soc 49(2):219~231
O. Garca-Prada / 2007 / Betti numbers of the moduli space of rank 3 parabolic Higgs bundles / Mem. Amer. Math. Soc. 187(879):1090
A. Lo Giudice / 2016 / A compactication of the moduli space of principal Higgs bundles over singular curves / J. Geom. Phys 110:328~342
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