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Pré-Publication, Document De Travail Année : 2017

Stability of restrictions of cotangent bundles of hypersurfaces

Résumé

Let $Y\subset\mathbb{P}^{n+1}$ be a general smooth hypersurface of dimension $\geq 3$. It is well-known that the cotangent bundle $\Omega_Y^1$ is stable. In this note, we prove that the restriction $\Omega_Y^1|_X$ over a general smooth hypersurface $X$ of $Y$ with $Pic(Y)\cong Pic(X)$ is stable except for some well-known examples. We also address the cases where the Picard group increases by restriction.

Dates et versions

hal-01635599 , version 1 (15-11-2017)

Identifiants

Citer

Jie Liu. Stability of restrictions of cotangent bundles of hypersurfaces. 2017. ⟨hal-01635599⟩
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