Reading Seminar on Moduli of Abelian Varieties





The Reading Seminar on moduli of abelian varieties will take place Tuesdays 16:00-17:00 in A410.



Description

This semester the goal is to study the Torelli map and Toroidal compactifications of Ag. The goal is to understand Alexeev - Brunyate's proof that the Torelli map extends to the perfect cone compactifications. Here is a rough outline of the seminar.


Schedule of upcoming talks

April 16
NO SEMINAR
April 23
David Ploog Background on toroidal compactifications
April 30
David Ploog Background on toroidal compactifications
May 7
NO TALK GO TO BAS'S TALK
May 14
David Ploog Background on toroidal compactifications
May 21
Malte Wandel Cone of positive semidefinite quadratic forms
May 28
Jesse Kass Toroidal compactifications of A_2
June 4
Nicola Pagani Toroidal compactifications of A_2
June 11
Nicola Tarasca The Torelli map into the 2nd Voronoi compactification
June 18
Nicola Tarasca The Torelli map into the 2nd Voronoi compactification
June 25
Jesse Kass Criteria for the Torelli map to extend
July 2
Davide Veniani The Torelli map into the central cone compactification
July 9
Jesse Kass Alternative extensions of the Torelli map

Notes

(1) "Toroidal compactifications of A_2" by Jesse Kass. (5 June, 2013)
(2) "Toroidal compactifications" by David Ploog (6 June, 2013)
(3) "Cone of quadratic forms" by Malte Wandel (6 June, 2013)
(4) "The Torelli map and the 2nd Voronoi compactification" by Nicola Tarasca (17 June, 2013)
(5) "Criteria to extend the Torelli map" by Jesse Kass (1 July, 2013)

References

References for toroidal compactifications:
(1) "A new compactification of the Siegel space and degeneration of Abelian varieties. I" by Namikawa
(2) "A new compactification of the Siegel space and degeneration of Abelian varieties. II" by Namikawa
(3) "Toroidal compactification of Siegel spaces" by Namikawa
(4) "On the canonical holomorphic map from the moduli space of stable curves to the Igusa monoidal transform" by Namikawa
(5) "The geometry of Siegel modular varieties" by Hulek and Sankaran
(5) "Degenerations of abelian varieties: Notes from Pragmatic Summer School" by Hulek
(6) "Sur la compactification de Satake" by Cartan

References for cone of positive semidefinite quadratic forms:
(1) "Comparing perfect and 2nd Voronoi decompositions: the matroidal locus" by Melo and Viviani
(2) See the Namikawa articles and the references found there.

References for the Torelli map into the 2nd Voronoi compactification:
(1) See the Namikawa articles.

References for the Torelli map into the perfect cone compactification:
(1) "Extending the Torelli map to toroidal compactifications of Siegel space" by Alexeev and Brunyate
(2) "Extended Torelli map to the Igusa blowup in genus 6, 7, and 8" by Alexeev, Livingston, Tenini, Arap, Hu, Huckaba, McFaddin, Musgrave, Shin, and Ulrich