On the three compactifications of Siegel space

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• Valery Alexeev (Georgia)
• Wednesday 02 March 2011, 14:15-15:15
• MR13, CMS.

If you have a question about this talk, please contact Burt Totaro.

The moduli space A_g of abelian varieties has three classical toroidal compactifications: (1) perfect, (2) 2nd Voronoi, and (3) Igusa blowup, each with its own distinct geometric meaning. It is an interesting problem to understand exactly how these compactifications are related.

I will show that (1) and (2) are isomorphic in a neighborhood of the image of a regular map from Deligne-Mumford’s moduli space M_g bar, and that the rational map from M_g bar to A_g bar for (3) is not regular. This is a joint work with Adrian Brunyate.

This talk is part of the Algebraic Geometry Seminar series.

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