Tangent bundle of hypersurfaces in G/P

Biswas, Indranil ; Schumacher, Georg (2009) Tangent bundle of hypersurfaces in G/P Journal of K-Theory, 4 (1). pp. 91-100. ISSN 1865-2433

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Official URL: http://journals.cambridge.org/abstract_S1755069608...

Related URL: http://dx.doi.org/10.1017/is008002001jkt052


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 dim G/P ≤ p. Let L : H →G/P be a reduced smooth hypersurface in G/P of degree d. We will assume that the pullback homomorphism Z = Pic(G/P) →i* Pic(H) 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 d > τ (G/P)(n-1)/ 2n-1 ( hold; here n = dimH, and T (G/P)∈ N is the index of G/P which is defined by the identity K-1G/P= L ⊗τG/P where L is the ample generator of Pic(G/P) and K-1 G/P 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 ρ > 0, and τG/P > d > τ(G/P)(n-1)/ 2n-1, then TH is strongly stable. If p > 0, and d = τ(G/P), then TH is strongly semistable.

Item Type:Article
Source:Copyright of this article belongs to Cambridge University Press.
Keywords:Homogeneous space; Hypersurface; Stable tangent bundle
ID Code:3555
Deposited On:12 Oct 2010 04:16
Last Modified:12 Oct 2010 04:16

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