Reading seminar on the geometry of the moduli space of polarized abelian varieties and its compactifications

The goal of this seminar would be to:

1. Review the moduli of abelian varieties and how they degenerate
2. Understand the construction of its toroidal compactifications, using inputs from tropical and logarithmic geometry
3. Study different topics that arise naturally:intersection theory on these moduli spaces, the compactification interesting loci from $\mathcal {A}_g$, logarithmic abelian varieties and some arithmetic side of the whole story.

The lectures will be held on Wednesdays, mostly from 13:30 to 15:00 in the Hermann Weyl room HG G 43, and we invite everyone to join, wether they give a lecture or not.

We will be recording the lectures and invite the speakers to write down some extended notes from the talk to include everything in a final document.

The schedule so far is the following

Link to the overleaf project with extended notes:

Some topics that we are considering and don't have a lecturer are:

• Compactifications of the universal abelian variety.
• Compactification of special cycles and the birational geometry of $\mathcal{A}_g$.
• Logarithmic Chow rings and Pixton's conjecture for $\lambda_g$.
• Fourier-Mukai transforms and applications.
• Intersection theory on some partial toroidal compactifications.
• Moduli of log abelian varieties.
• Local systems and the cohomology of $\mathcal{A}_g$.
• Neron models.

We want to invite some experts from outside ETH to talk about some of them.

Organizers

• Samir Canning
• Aitor Iribar Lopez
• Johannes Schmitt

General references:

• [1] The cohomology of the Moduli space of Abelian Varieties Gerard van der Geer (https://arxiv.org/pdf/1112.2294)
• [2] Toroidal Compactifications of Siegel Spaces Yukio Namikawa (https://link.springer.com/book/10.1007/BFb0091051)