Intercity Seminar 'Functorial compactification of moduli of abelian varietes',
Fall 2010
Aim
In 2002 V. Alexeev gave a functorial compactification of the moduli space of polarized abelian varieties motivated by, among many others, ideas from the early seventies due to D. Mumford. The boundary parametrizes so-called 'stable semiabelic pairs'. The compactification given by Alexeev has several irreducible components, and one wants to give a functorial description of the 'main component' containing the moduli space of abelian varieties. A solution to this problem has been given by M. Olsson in 2007, using log structures. The aim of this IC Seminar is to understand these developments.
Organizers: Jochen Heinloth and Robin de Jong.
Programme
- Friday September 17, 2010, Universiteit Leiden, Snellius building, Room B1.
11:00-12:45 Robin de Jong: Introduction, statement of main results
14:00-15:45 Jochen Heinloth: Algebraic stacks
- Friday October 22, 2010, University of Amsterdam, Korteweg-de Vries Institute, Science Park 904.
11:00-12:45 Lenny Taelman: Linearization of torus actions (Room C1.112 - ascend a small stairs left of the porter's lodge)
14:00-15:45 Jan Stienstra: Linearization of semiabelian group actions (Room A1.114)
- Friday November 5, 2010, Universiteit Utrecht, Minnaert Building, Room 019 (descend a small stairs from the middle of the central hall).
11:00-12:45 Gerard van der Geer: Alexeev's construction
14:00-15:45 Ben Moonen: Introduction to log geometry
- Friday November 12, 2010, Universiteit Leiden, Snellius building, Room B1.
11:00-12:45 Bas Edixhoven: Olsson's standard family and moduli problem I, notes.
14:00-14:45 Bas Edixhoven: Olsson's standard family and moduli problem II
15:00-15:45 Franziska Heinloth: Deformations and versal families
- Friday December 3, 2010, Universiteit van Amsterdam, Roeterseilandcomplex.
11:00-11:45 Franziska Heinloth: Versal families for the moduli problem (Room A2.23, Building A, Roetersstraat 15)
12:00-12:45 Lenny Taelman: Properness I
14:00-14:45 Robin de Jong: Properness II (Room P0.18, Building P, Plantage Muidergracht 24)
15:00-15:45 Jochen Heinloth: Olsson's moduli problem defines an algebraic stack
Links
Here are links to relevant literature.
D. Abramovich, Q. Chen, D. Gillam, Y. Huang, M. Olsson, M. Satriano, S. Sun,
Logarithmic geometry and moduli.
V. Alexeev, Complete moduli in the presence of semiabelian group action.
G. Faltings, C.-L. Chai, Degeneration of abelian varieties.
D. Mumford, An analytic construction of degenerating abelian varieties over complete rings.
A. Ogus, Lectures on logarithmic algebraic geometry.
M. Olsson, Compactifying moduli spaces for abelian varieties.
A seminar held at the University of Duisburg-Essen on the same subject.