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Mathematics > Algebraic Geometry

arXiv:1508.07716 (math)
[Submitted on 31 Aug 2015 (v1), last revised 30 Oct 2016 (this version, v2)]

Title:Canonical Kahler metrics and Arithmetics -- Generalising Faltings heights

Authors:Yuji Odaka
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Abstract:We extend the Faltings modular heights of abelian varieties to general arithmetic varieties and show direct relations with the Kahler-Einstein geometry, the Minimal Model Program, heights of Bost and Zhang, and give some applications. Along the way, we propose arithmetic Yau-Tian-Donaldson conjecture, an equivalence of a purely arithmetic property of variety and its metrical property, and partially confirm it.
Comments: 47 pages. Final version, to appear in Kyoto Journal of Mathematics
Subjects: Algebraic Geometry (math.AG); Differential Geometry (math.DG); Number Theory (math.NT)
Cite as: arXiv:1508.07716 [math.AG]
  (or arXiv:1508.07716v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1508.07716
Journal reference: Kyoto J. Math. 58, no. 2 (2018), 243-288
Related DOI: https://doi.org/10.1215/21562261-2017-0023

Submission history

From: Yuji Odaka [view email]
[v1] Mon, 31 Aug 2015 08:30:52 UTC (40 KB)
[v2] Sun, 30 Oct 2016 08:31:10 UTC (43 KB)
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