Lagrangian submanifolds in Hyperkahler manifolds, Legendre transformation

Details Lagrangian submanifolds in Hyperkahler manifolds, Legendre transformation Lagrangian submanifolds in Hyperkahler manifolds, Legendre transformation

2001-10-31

arxiv.org/abs/math/0110330v1

Mathematics

Symplectic Geometry

43 pages

Scientific paper

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.

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