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I've been working on reading and understanding Arakelov's '71 paper and he uses the fact that the moduli space of complex abelian varieties of dimension $g$ with polarization of degree $d$ admits an embedding into some projective space $\mathbb{P}_{\mathbb{C}}^N$ by modular forms of weight $m >\!\!> 0$. My understanding is this is a consequence of Satake/Baily-Borel compactification but I'd like to see the details of this, as it's pretty far outside of my wheelhouse. Are there any self-contained explanations of this?

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  • $\begingroup$ A self-contained explanation of an even stronger result is Moret-Bailly's Asterisque "Pinceaux de varietes abeliennes" ; see numdam.org/issue/AST_1985__129__1_0.pdf $\endgroup$ – Ariyan Javanpeykar Nov 2 '19 at 22:26
  • $\begingroup$ @AriyanJavanpeykar: Do you have a more precise reference? The book has 269 pages, so some pointer is needed... $\endgroup$ – Bombyx mori Nov 17 '19 at 5:22

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