# Complete symplectic quadrics and Kontsevich moduli spaces of conics in Lagrangian Grassmannians

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Alex Massarenti

created by bazzoni on 09 Nov 2021

modified on 14 Dec 2021

15 dec 2021
-- 17:00

Geometry in Como - online

**Abstract.**

Given a reductive algebraic group G and a Borel subgroup B, a spherical variety is a normal variety admitting an action of G with an open dense B-orbit. A special class of spherical varieties are the so-called wonderful varieties. These are smooth spherical varieties for which we require G to be semisimple and simply connected and the existence of an open B-orbit whose complementary set is a simple normal crossing divisor. We will construct the wonderful compactification of the space of symmetric, symplectic matrices on which the symplectic group acts. Furthermore, we will compute the Picard group of this compactification and we will study its birational geometry in low-dimensional cases. As an application, we will recover the results on the birational geometry of the Kontsevich spaces of conics in Grassmannians due to I. Coskun a D. Chen, and we will prove new results on the birational geometry of the Kontsevich spaces of conics in Lagrangian Grassmannians.

This is a joint work with Elsa Corniani.