The moduli space of curves has a compactification whose boundary can be understood as the product of moduli spaces of curves of lower genus. Therefore (perhaps naively) one might hope that there exists a compactification of $A_g$ whose boundary can be understood as in terms of the moduli of abelian varieties of lower dimension. Is there any such compactification?
$\begingroup$
$\endgroup$
4
-
6$\begingroup$ There are many! This is a long chapter of algebraic geometry. You might have a look at this paper for instance to get some idea. $\endgroup$– abxCommented Jul 29, 2020 at 4:26
-
7$\begingroup$ The minimal ("Baily-Borel-Satake") compactification of $\mathcal{A}_g$ has boundary $\coprod_{i<g} \mathcal{A}_i$ (with a certain topology). Maybe that's the sort of thing you want? $\endgroup$– David HansenCommented Jul 29, 2020 at 10:28
-
$\begingroup$ Thank you very much to the both of you! This is exactly what I wanted! $\endgroup$– curious math guyCommented Jul 29, 2020 at 14:38
-
2$\begingroup$ I unprotected this question because it seems the only reason it got protected was that it happened to be hit by two spam answers by one user, and because I don't see a reason that this question is more likely to receive further spam answers than just any other question. $\endgroup$– Stefan Kohl ♦Commented Aug 22, 2020 at 10:08
Add a comment
|