Deformations of Lagrangian subvarieties of holomorphic symplectic manifolds

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Lehn, Christian;
  • Subject: 53D05, 32G10, 13D10, 14C30 | Mathematics - Algebraic Geometry
    arxiv: Mathematics::Algebraic Geometry | Mathematics::Complex Variables | Mathematics::Symplectic Geometry

We generalize Voisin's theorem on deformations of pairs of a symplectic manifold and a Lagrangian submanifold to the case of Lagrangian normal crossing subvarieties. Partial results are obtained for arbitrary Lagrangian subvarieties. We apply our results to the study of... View more
  • References (1)

    Gang Tian. Smoothness of the universal deformation space of compact Calabi-Yau manifolds and its Petersson-Weil metric. In Mathematical aspects of string theory, pages 629{646. World Sci. Publishing, Singapore, 1987. { cited on p. 1, 8 Andrey N. Todorov. The Weil-Petersson geometry of the moduli space of SU(n 3) (Calabi-Yau) manifolds. I. Comm. Math. Phys., 126(2):325{346, 1989. { cited on p. 1, 8 Claire Voisin. Sur la stabilite des sous-varietes lagrangiennes des varietes symplectiques holomorphes. In Complex projective geometry, pages 294{ 303. Cambridge Univ. Press, 1992. { cited on p. 1, 2, 9, 10, 22 Claire Voisin. Hodge theory and complex algebraic geometry. I, Cambridge University Press, Cambridge, 2002. { cited on p. 12 Claire Voisin. Hodge theory and complex algebraic geometry. II, Cambridge University Press, Cambridge, 2003. { cited on p. 8

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