Canonical Kahler metrics and arithmetics: Generalizing Faltings heights

被引：2
作者：
Odaka, Yuji [1 ]
机构：
[1] Kyoto Univ, Dept Math, Kyoto 6068502, Japan
来源：
KYOTO JOURNAL OF MATHEMATICS | 2018年 / 58卷 / 02期
基金：
日本学术振兴会;
关键词：
COMPACT MODULI SPACES; HODGE INDEX THEOREM; EINSTEIN METRICS; SCALAR CURVATURE; K-STABILITY; PROJECTIVE EMBEDDINGS; ANALYTIC-TORSION; STABLE VARIETIES; RICCI FLOW; MANIFOLDS;
D O I：
10.1215/21562261-2017-0023
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We extend the Faltings modular heights of Abelian varieties to general arithmetic varieties, show direct relations with the Kahler-Einstem geometry, the minimal model program, and Bost-Zhang's heights and give some applications Along the way, we propose the "arithmetic Yau-Tian-Donaldson conjecture" (the equivalence of a purely arithmetic property of a variety and its metrical property) and partially confirm it.
引用
收藏
页码：243 / 288
页数：46
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