École polytechnique  – Centre de Mathématiques Laurent Schwartz

Mardi 25 septembre 2024

14h00 : Kwon Minseong (Kaist, Séoul)

"Spaces of conics on adjoint varieties "

Abstract: 
Rational homogeneous spaces are complex projective manifolds containing a plenty of rational curves, and geometry of lines lying on them is well-understood. In this talk, I will discuss geometry of conics on adjoint varieties, which are rational homogeneous spaces arising from the adjoint representations of simple Lie algebras. First, I will recall the definition of adjoint varieties, together with some examples. A distinguished structure of the adjoint varieties, called contact structure, will be also introduced. Next, I will explain how we can describe the Hilbert schemes of conics on adjoint varieties using contact geometry and the embedding theory of spherical varieties.