Deformations of the tangent bundle of a projective hypersurface

Insong Choe; Kiryong Chung; Jun-Muk Hwang

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arXiv · 2506.20085

Deformations of the tangent bundle of a projective hypersurface

Insong Choe·Kiryong Chung·Jun-Muk Hwang

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Abstract

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.

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BibTeX RIS

Insong Choe, Kiryong Chung, Jun-Muk Hwang. 2025-06-25. Deformations of the tangent bundle of a projective hypersurface. https://arxiv.org/abs/2506.20085

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