About the stability of the tangent bundle of Pⁿ restricted to a surface

2009/06/10 by Chiara Camere, Camere, Chiara
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.0906.1966

arxiv created 2009/06/10 · openalex publication_date 2009/06/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth projective surface over C and let L be a line bundle on X generated by its global sections. Let f:X-->P^r be the morphism associated to L and let T be the tangent bundle of P^r; we investigate the μ-stability of f*T with respect to L when X is either a regular surface with p_g=0, a K3 surface or an abelian surface. In particular, we show that it is μ-stable when X is K3 and L is ample and when X is abelian and L²>13.

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