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Tangent bundle of hypersurfaces in G/P

Published online by Cambridge University Press:  12 May 2008

Indranil Biswas  and
Georg Schumacher
Indranil Biswas
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India, indranil@math.tifr.res.in.
Georg Schumacher
Affiliation:
Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Lahnberge, Hans-Meerwein-Strasse, D-35032 Marburg, Germany, schumac@mathematik.uni-marburg.de.
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Abstract

Let G be a simple linear algebraic group defined over an algebraically closed field k of characteristic p ≥ 0, and let P be a maximal proper parabolic subgroup of G. If p > 0, then we will assume that dimG/P ≤ p. Let ι : H ↪ G/P be a reduced smooth hypersurface in G/P of degree d. We will assume that the pullback homomorphism is an isomorphism (this assumption is automatically satisfied when dimH ≥ 3). We prove that the tangent bundle of H is stable if the two conditions τ(G/P) ≠ d and hold; here n = dimH, and τ(G/P) ∈ is the index of G/P which is defined by the identity = where L is the ample generator of Pic(G/P) and is the anti–canonical line bundle of G/P. If d = τ(G/P), then the tangent bundle TH is proved to be semistable. If p > 0, and then TH is strongly stable. If p > 0, and d = τ(G/P), then TH is strongly semistable.

Keywords

Homogeneous spacehypersurfacestable tangent bundle
Type
Research Article
Information
Journal of K-Theory , Volume 4 , Issue 1 , August 2009 , pp. 91 - 100
Copyright
Copyright © ISOPP 2008

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