Lecturer: Nicolas Perrin
I will introduce spherical varieties which are generalisations of both toric varieties and homogeneous spaces. I will explain the combinatorial invariants associated to spherical varieties and their embeddings. I shall also discuss their classification and some of their geometric properties.
References:
1. Fulton, W. Introduction to Toric varieties. Ann. of Mathematical Studies 131, Princeton Univ. Press, 1993.
2. Timashev, D.: Homogeneous spaces and equivariant embeddings. In: Encyclopaedia of Mathematical Sciences 138, Springer, Berlin.
2. Brion, M. Variétés sphériques (ps, pdf) Notes de la session de la S. M. F. "Opérations hamiltoniennes et opérations de groupes algébriques" (Grenoble, 1997), 59 pages.
3. Brion, M. Spherical varieties (ps, pdf) Notes de l'école d'été "Structures in Lie Representation Theory" (Bremen, 2009), 24 pages.
4. Gandini, J. Embeddings of spherical homogeneous spaces. PDF
5. Knop, F. The Luna-Vust Theory of Spherical Embeddings, pp. 225-249. In: Proceedings of the Hyderabad Conference on Algebraic Groups, Manoj-Prakashan 1991.
6. Perrin, N. On the geometry of spherical varieties, Transform. Groups 19 (2014), no. 1, 171-223.
7. Perrin, N. Sanya Lectures: Geometry of Spherical varieties. PDF or https://arxiv.org/abs/1705.10204