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Stabilité des images inverses des fibrés tangents et involutions des variétés symplectiques

Abstract : Abstract : This thesis consists of two independent parts about two different problems in Algebraic Geometry. In the first part we study the stability of inverse images of the tangent bundle of the projective space over projective varieties. The stability of these bundles turns out to be equivalent to the stability of the kernel of the evaluation map ML of a line bundle L generated by its global sections. We obtain an optimal result in the case of projective curves and then we apply it to get the stability in the case of some projective surfaces, such as K3 and abelian surfaces. The second problem we deal with is the study of fixed points of a symplectic involution over an irreducible holomorphic symplectic manifold of dimension 4 such that b2 = 23. We show that there are only 3 possibilities for the number of fixed points and of fixed K3 surfaces. We conjecture that only one case can actually occurr, the one with 28 isolated fixed points and 1 fixed K3 surface, and that such an involution can never fix an abelian surface. We provide evidences for the conjecture by verifying it in some examples.
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Contributor : Chiara Camere <>
Submitted on : Thursday, January 6, 2011 - 12:05:57 PM
Last modification on : Monday, October 12, 2020 - 10:27:29 AM
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  • HAL Id : tel-00552994, version 1



Chiara Camere. Stabilité des images inverses des fibrés tangents et involutions des variétés symplectiques. Mathématiques [math]. Université Nice Sophia Antipolis, 2010. Français. ⟨tel-00552994⟩



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