Deformations of the tangent bundle of a projective hypersurface
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915358208688128 |
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| author | Choe, Insong Chung, Kiryong Hwang, Jun-Muk |
| author_facet | Choe, Insong Chung, Kiryong Hwang, Jun-Muk |
| contents | For a nonsingular hypersurface $X \subset \mathbb{P}^n, n \geq 4,$ of degree $d \geq 2$, we show that the space $H^1(X, \End(T_X))$ of infinitesimal deformations of the tangent bundle $T_X$ has dimension ${n+d-1 \choose d} (d-1)$ and all infinitesimal deformations are unobstructed even though $H^2(X, \End(T_X))$ can be nonzero. Furthermore, we prove that the irreducible component of the moduli space of stable bundles containing the tangent bundle is a rational variety, by constructing an explicit birational model. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_20085 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deformations of the tangent bundle of a projective hypersurface Choe, Insong Chung, Kiryong Hwang, Jun-Muk Algebraic Geometry 14J60, 14J70, 14D20 For a nonsingular hypersurface $X \subset \mathbb{P}^n, n \geq 4,$ of degree $d \geq 2$, we show that the space $H^1(X, \End(T_X))$ of infinitesimal deformations of the tangent bundle $T_X$ has dimension ${n+d-1 \choose d} (d-1)$ and all infinitesimal deformations are unobstructed even though $H^2(X, \End(T_X))$ can be nonzero. Furthermore, we prove that the irreducible component of the moduli space of stable bundles containing the tangent bundle is a rational variety, by constructing an explicit birational model. |
| title | Deformations of the tangent bundle of a projective hypersurface |
| topic | Algebraic Geometry 14J60, 14J70, 14D20 |
| url | https://arxiv.org/abs/2506.20085 |