Legendrian varieties

Details Legendrian varieties Legendrian varieties

2004-07-15

arxiv.org/abs/math/0407279v1

Mathematics

Algebraic Geometry

21 pages

Scientific paper

We investigate the geometry of Legendrian complex projective manifolds $X\subset\PP V$. By definition, this means $V$ is a complex vector space of dimension $2n+2$, endowed with a symplectic form, and the affine tangent space to $X$ at each point is a maximal isotropic subspace. We establish basic facts about their geometry and exhibit examples of inhomogeneous smooth Legendrian varieties, the first examples of such in dimension greater than one.

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