PreprintarXiv licencearXiv
Infinitesimal Deformations of Generalized Parabolic Hitchin Pairs
Abstract
We develop the infinitesimal deformation theory of generalized parabolic Hitchin pairs (GPHs) on irreducible nodal curves. For any GPH $(E,Ο,F(E))$ we associate an explicit three-term deformation complex π(Eβ’,Ο) whose first hypercohomology β1(π(Eβ’,Ο)) parameterizes first-order deformations. As the main application, we prove that the coarse moduli space β³GPH of $1$-stable generalized parabolic Hitchin pairs of rank n and degree d with gcd(n,d)=1 is a local complete intersection, smooth in codimension one, and hence a normal variety. We further show that this moduli space carries a natural Poisson structure.
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BibTeX
@misc{das2026infinitesimal,
title = {{Infinitesimal Deformations of Generalized Parabolic Hitchin Pairs}},
author = {Sourav Das},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29780},
eprint = {2608.29780},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29780},
}
RIS
TY - UNPB
TI - Infinitesimal Deformations of Generalized Parabolic Hitchin Pairs
AU - Sourav Das
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29780
UR - https://arxiv.org/abs/2608.29780
AB - We develop the infinitesimal deformation theory of generalized parabolic Hitchin pairs (GPHs) on irreducible nodal curves. For any GPH $(E,Ο,F(E))$ we associate an explicit three-term deformation complex π_(E_β’,Ο) whose first hypercohomology β^1(π_(E_β’,Ο)) parameterizes first-order deformations. As the main application, we prove that the coarse moduli space β³_GPH of $1$-stable generalized parabolic Hitchin pairs of rank n and degree d with gcd(n,d)=1 is a local complete intersection, smooth in codimension one, and hence a normal variety. We further show that this moduli space carries a natural Poisson structure.
ER -