%0 Journal Article %1 leung_lagrangian_2001 %A Leung, Naichung Conan %D 2001 %J math/0110330 %K Geometry Symplectic %T Lagrangian submanifolds in Hyperkahler manifolds, Legendre transformation %U http://arxiv.org/abs/math/0110330 %X We develop the foundation of the complex symplectic geometry of Lagrangian subvarieties in a hyperkahler manifold. We establish a characterization, a Chern number inequality, topological and geometrical properties of Lagrangian submanifolds. We discuss a category of Lagrangian subvarieties and its relationship with the theory of Lagrangian intersection. We also introduce and study extensively a normalized Legendre transformation of Lagrangian subvarieties under a birational transformation of projective hyperkahler manifolds. We give a Plucker type formula for Lagrangian intersections under this transformation.

@article{leung_lagrangian_2001, abstract = {We develop the foundation of the complex symplectic geometry of Lagrangian subvarieties in a hyperkahler manifold. We establish a characterization, a Chern number inequality, topological and geometrical properties of Lagrangian submanifolds. We discuss a category of Lagrangian subvarieties and its relationship with the theory of Lagrangian intersection. We also introduce and study extensively a normalized Legendre transformation of Lagrangian subvarieties under a birational transformation of projective hyperkahler manifolds. We give a Plucker type formula for Lagrangian intersections under this transformation.}, added-at = {2009-05-11T21:36:02.000+0200}, author = {Leung, Naichung Conan}, biburl = {https://www.bibsonomy.org/bibtex/25dd0f9d41673b1bd4f70d4ebc47a8b3a/tbraden}, interhash = {8d0d4382cd41eff4fd9a62ccba39f443}, intrahash = {5dd0f9d41673b1bd4f70d4ebc47a8b3a}, journal = {math/0110330}, keywords = {Geometry Symplectic}, month = {October}, timestamp = {2009-05-11T21:36:02.000+0200}, title = {Lagrangian submanifolds in Hyperkahler manifolds, Legendre transformation}, url = {http://arxiv.org/abs/math/0110330}, year = 2001 }