course: Compact moduli of higher-dimensional varieties

speaker: Valery Alexeev (University of Georgia)

abstract: The most famous geometrically meaningful compactifications of moduli spaces of varieties are Deligne-Mumford's moduli spaces of stable curves, and their generalizations to the relative case by Kontsevich and to the weighted case by Hassett. The Minimal Model Program offers a blueprint for extending the above to the case of higher dimensions. The lectures will concentrate on several recent examples where the program can be brought to fruition:

(1) varieties with group action (toric, abelian, spherical) (2) hyperplane arrangements (3) surfaces

Connections with the tropical geometry will be explored as well. The ideal prerequisites would be the familiarity with

(a) the one-dimensional case, e.g. Harris-Morrison's Moduli of Curves, another paper. (b) toric varieties, most importantly -- the interplay between projective toric varieties and polytopes, see e.g. Fulton's Introduction to Toric Varieties or Oda's Convex Bodies and Algebraic Geometry. (c) the singularities of pairs (X,B) appearing in the Minimal Model Program, such as log canonical and dlt, e.g. from Birational Geometry of Algebraic Varieties by Kollár and Mori.

timetable:
Mon 16 Jun, 15:15 - 16:15, Aula Dini
Tue 17 Jun, 15:15 - 16:15, Aula Dini
Thu 19 Jun, 15:15 - 16:15, Aula Dini
Fri 20 Jun, 15:15 - 16:15, Aula Dini
Sat 21 Jun, 9:00 - 9:50, Aula Dini
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