Spherical Geometry of Hilbert Schemes of Conics in Adjoint Varieties

Author:

Minseong Kwon

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Complex Variables (math.CV)

journal:

date:

2023-09-24 16:00:00

Abstract

For each adjoint variety not of type $A$ or $C$, we study the irreducible component of the Hilbert scheme which parametrizes all smooth conics. We prove that its normalization is a spherical variety by using contact geometry, and then compute the colored fan of the normalization. As a corollary, we describe the conjugacy classes of conics in the adjoint variety and show smoothness of the normalization. Similar results on the Chow scheme of the adjoint variety are also presented.

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