Projective aspects of the Geometry of Lagrangian Grassmannians and Spinor varieties

We study the projective behavior, mainly with respect to osculating spaces and secant varieties, of Lagrangian Grassmannians and Spinor varieties. We prove that these varieties have osculating dimension smaller than expected. Furthermore, we give numerical conditions ensuring the non secant defectiv...

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Bibliographic Details
Main Authors Freire, Ageu Barbosa, Massarenti, Alex, Rischter, Rick
Format Journal Article
LanguageEnglish
Published 18.12.2018
Subjects
Mathematics - Algebraic Geometry
Mathematics - Representation Theory
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Summary:We study the projective behavior, mainly with respect to osculating spaces and secant varieties, of Lagrangian Grassmannians and Spinor varieties. We prove that these varieties have osculating dimension smaller than expected. Furthermore, we give numerical conditions ensuring the non secant defectivity of Lagrangian Grassmannians in their Pl\"ucker embedding and of Spinor varieties in both their Pl\"ucker and Spinor embeddings.
DOI:10.48550/arxiv.1812.07474