具有$A_1$奇点的紧致复曲面的Almost-Kähler光滑性

IF 0.6 3区 数学 Q3 MATHEMATICS
Caroline Vernier
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引用次数: 3

摘要

本文研究了具有A1奇异点的常标量曲率Kahler轨道的光滑得到的几乎Kahler流形上常标量曲率度量的存在性。更准确地说,给定这样一个不允许非平凡全纯向量场的轨道,我们证明了一个几乎kahler平滑(Me, ωe)允许一个恒定厄米曲率的几乎kahler结构(Je, ge)。此外,我们证明了当e > 0足够小时,(Me, ωe)都辛等价于一个固定辛流形(M, ω),其中有一个曲面S与一个2球相对应,使得[S]是一个消失的循环,它允许一个对于ge是哈密顿平稳的表示。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Almost-Kähler smoothings of compact complex surfaces with $A_1$ singularities
This paper is concerned with the existence of metrics of constant Hermitian scalar curvature on almost-Kahler manifolds obtained as smoothings of a constant scalar curvature Kahler orbifold, with A1 singularities. More precisely, given such an orbifold that does not admit nontrivial holomorphic vector fields, we show that an almost-Kahler smoothing (Me, ωe) admits an almost-Kahler structure (Je, ge) of constant Hermitian curvature. Moreover, we show that for e > 0 small enough, the (Me, ωe) are all symplectically equivalent to a fixed symplectic manifold (M , ω) in which there is a surface S homologous to a 2-sphere, such that [S] is a vanishing cycle that admits a representant that is Hamiltonian stationary for ge.
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
0
审稿时长
>12 weeks
期刊介绍: Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.
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