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- W2156477024 abstract "Let X be a compact Riemann surface of genus g>1. We study two different, naturally defined metric forms on X: The hyperbolic metric form μ hyp, X , arising from hyperbolic geometry, and the Arakelov metric form μ Ar, X , arising from arithmetic algebraic geometry. Now consider a sequence X t of Riemann surfaces approaching the Deligne-Mumford boundary of the moduli space of compact Riemann surfaces of genus g. We prove here that As a corollary of this result, we prove that the Weil-Petersson metric on the moduli space induced from the Arakelov metric is not complete, i.e., certain boundary components of the Deligne-Mumford compactification are at finite distance." @default.
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- W2156477024 date "2006-02-07" @default.
- W2156477024 modified "2023-09-27" @default.
- W2156477024 title "Non-completeness of the Arakelov-induced metric on moduli space of curves" @default.
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- W2156477024 doi "https://doi.org/10.1007/s00229-006-0625-2" @default.
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