Tropical Geometric Compactification of Moduli, II - A_g case and holomorphic limits - [article]

Yuji Odaka
2017 arXiv   pre-print
We compactify the classical moduli variety A_g of principally polarized abelian varieties of complex dimension g by attaching the moduli of flat tori of real dimensions at most g in an explicit manner. Equivalently, we explicitly determine the Gromov-Hausdorff limits of principally polarized abelian varieties. This work is analogous to the first of our series (available at arXiv:1406.7772v2), which compactified the moduli of curves by attaching the moduli of metrized graphs. Then, we also
more » ... itly specify the Gromov-Hausdorff limits along holomorphic family of abelian varieties and show that they form special non-trivial subsets of the whole boundary. We also do it for algebraic curves case and observe a crucial difference with the case of abelian varieties.
arXiv:1705.05545v1 fatcat:vhnhl6hag5dcjbop5racbkbu6e