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6 votes

Height functions on $\mathcal{M}_g(\overline{\Bbb{Q}})$ defined via dessins d'enfants?

If I am not mistaken, this precise issue was attacked by Dirk Smit during 1990s in a series of papers on Communications of Mathematical Physics. I am not sure why his papers are not quoted more widely …
Bombyx mori's user avatar
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5 votes
1 answer
366 views

Deligne's example of $\deg \pi_{*}\Omega_{X/Y}<0$

While reviewing Lang's book on Arakelov theory, I saw the following comment by Paul Vojta: "...Deligne has found an example when $\deg \pi_{*}\Omega_{X/Y}$ can be negative, because Green's functions …