Restriction theorems for homogeneous bundles

2004/11/29 by V. B. Mehta, Mehta, V. B., V. Trivedi +1
Mathematics · #14L30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:14L30

paper · pdf · doi:10.48550/arxiv.math/0411629

Revised version contains a stronger result:strong semistability is proved for restrictions to generic hypersurfaces of arbitrary degree >1, instead of generic hypersurfaces of even degree

arxiv created 2005/03/30 · arxiv updated 2009/12/01

Abstract

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

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