Restriction theorems for homogeneous bundles

Details Restriction theorems for homogeneous bundles Restriction theorems for homogeneous bundles

2004-11-29

arxiv.org/abs/math/0411629v2

Mathematics

Algebraic Geometry

Revised version contains a stronger result:strong semistability is proved for restrictions to generic hypersurfaces of arbitra

Scientific paper

We prove that for an irreducible representation $\tau:GL(n)\to GL(W)$, the associated homogeneous ${\bf P}_k^n$-vector bundle $W_{\tau}$ 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 $W_{\tau}$ 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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