Collapsing hyperkähler manifolds

IF 1.3 1区数学 Q1 MATHEMATICS

Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2017-05-09 DOI:10.24033/ASENS.2433

Valentino Tosatti, Yuguang Zhang

引用次数: 20

Abstract

Given a projective hyperkahler manifold with a holomorphic Lagrangian fibration, we prove that hyperkahler metrics with volume of the torus fibers shrinking to zero collapse in the Gromov-Hausdorff sense (and smoothly away from the singular fibers) to a compact metric space which is a half-dimensional special Kahler manifold outside a singular set of real Hausdorff codimension 2 and is homeomorphic to the base projective space.

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坍塌hyperkähler流形

给出一个具有全纯拉格朗日纤维的射影超Kahler流形，证明了具有环面纤维体积的超Kahler流形在Gromov-Hausdorff意义上收缩到零坍缩(并且平滑地远离奇异纤维)到紧度量空间，该空间是位于实Hausdorff余维数2的奇异集之外的半维特殊Kahler流形，并且与基射影空间同胚。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annales Scientifiques De L Ecole Normale Superieure 数学-数学

CiteScore

3.00

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics. Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition. The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.