拟多次谐波包络2:蒙日-安培体积上的界

IF 1.2 1区数学 Q1 MATHEMATICS

Algebraic Geometry Pub Date : 2021-06-08 DOI:10.14231/AG-2022-021

V. Guedj, C. H. Lu

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引用次数: 10

摘要

在｛GL21a｝中，我们开发了一种新的方法来求解$L^｛infty｝$——当参考形式闭合时退化复Monge-Amp方程的先验估计。该简化假设用于确保Monge Amp ere测量的体积恒定。我们在这里研究当参考形式不再闭合时，这些体积远离零和无穷大的方式。我们建立了Grauert-Riemenschneider猜想的超越版本，部分回答了Demaily-P\u的猜想{a}un\cite｛DP04｝和Boucksom-Demaily-P\u{a}un-Peternell\引用｛BDPP13｝。我们的方法依赖于准多亚谐波包络的精细使用。本文的结果将用于求解紧致Hermitian变种上的退化复Monge-Ampere方程。

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Quasi-plurisubharmonic envelopes 2: Bounds on Monge–Ampère volumes

In \cite{GL21a} we have developed a new approach to $L^{\infty}$-a priori estimates for degenerate complex Monge-Amp\`ere equations, when the reference form is closed. This simplifying assumption was used to ensure the constancy of the volumes of Monge-Amp\`ere measures. We study here the way these volumes stay away from zero and infinity when the reference form is no longer closed. We establish a transcendental version of the Grauert-Riemenschneider conjecture, partially answering conjectures of Demailly-P\u{a}un \cite{DP04} and Boucksom-Demailly-P\u{a}un-Peternell \cite{BDPP13}. Our approach relies on a fine use of quasi-plurisubharmonic envelopes. The results obtained here will be used in \cite{GL21b} for solving degenerate complex Monge-Amp\`ere equations on compact Hermitian varieties.

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来源期刊

Algebraic Geometry Mathematics-Geometry and Topology

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

52 weeks

期刊介绍： This journal is an open access journal owned by the Foundation Compositio Mathematica. The purpose of the journal is to publish first-class research papers in algebraic geometry and related fields. All contributions are required to meet high standards of quality and originality and are carefully screened by experts in the field.