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Restriction theorems for homogeneous bundles

V. B. Mehta·V. Trivedi
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Abstract

We prove that for an irreducible representation $τ:GL(n)\to GL(W)$, the associated homogeneous ${\bf P}_k^n$-vector bundle $W_τ$ is strongly semistable when restricted to any smooth quadric or to any smooth cubic in ${\bf P}_k^n$, where $k$ is an algebraically closed field of characteristic $\neq 2,3$ respectively. In particular $W_τ$ is semistable when restricted to general hypersurfaces of degree $\geq 2$ and is strongly semistable when restricted to the $k$-generic hypersurface of degree $\geq 2$.

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V. B. Mehta, V. Trivedi. 2005-03-30. Restriction theorems for homogeneous bundles. https://arxiv.org/abs/math/0411629

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