Winter School on Spherical Varieties


January 7 - 9, 2020                  Shilla Stay Haeundae, Busan

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◆ Lecture Series


Boris Pasquier (Poitiers)

- Title: Introduction to spherical varieties

- Abstract: The family of spherical varieties is one of the biggest family of examples of complex algebraic varieties, including the family of toric varieties that are very-well understood and appear in a lot of works in algebraic geometry. The aim of this lecture is to explain how the theory of toric varieties extends to a larger family of varieties endowed with an action of a connected reductive algebraic group.  We will begin by recalling the theory of toric varieties and the basics of linear actions of reductive groups.



◆ Seminar Talks


Benoit Dejoncheere (Alberta)

- Title: An introduction to Grothendieck-Cousin complexes

- Abstract: Let X be a complex algebraic variety. In this talk, I will introduce the Grothendieck-Cousin complexes associated to a filtration of X by closed subsets, and we will discuss some interesting properties they have when the filtration satisfies mild conditions. We will then focus on several examples in the world of spherical G-varieties, where we can build a nice filtration using the action of a Borel subgroup B of G.


Giuliano Gagliardi (Hannover)

- Title: "Existence of equivariant models of spherical varieties".

- Abstract: This refers to recent joint work with Mikhail Borovoi on the existence of spherical varieties over arbitrary fields of characteristic 0.


Qifeng Li (KIAS)

- Title: Rigidity of wonderful compactifications of simple groups under Fano deformation

- Abstract: Let G be a simple complex linear algebraic group of adjoint type. It admits a wonderful compactification, denoted by X. We will explain basic properties of X, and then discuss its rigidity under Fano deformation. This talk is based on the joint work with Baohua Fu.


Clelia Pech (Kent)

- Title: Quantum cohomology for horospherical varieties with Picard rank one.

- Abstract: Horospherical varieties with Picard rank one are a particularly interesting family of spherical varieties which have been classified by Pasquier in 2008. In this talk I will explain the construction of these varieties and present joint results with Gonzales, Perrin and Samokhin on their quantum cohomology. If time allows I will also explain some results concerning their derived category of coherent sheaves.



Organized by Jun-Muk Hwang (KIAS)


Supported by National Researcher Program (NRF)