Some quasihomogeneous Legendrian varieties

Mathematics – Algebraic Geometry

Scientific paper

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21 pages, 1 figure

Scientific paper

We construct a family of examples of Legendrian subvarieties in some
projective spaces. Although most of them are singular, a new example of smooth
Legendrian variety in dimension 8 is in this family. The 8-fold has interesting
properties: it is a compactification of the special linear group, a Fano
manifold of index 5 and Picard number 1.

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