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

页码：243 / 288

页数：46