K3${}^{[n]}$型低维超kähler流形上的MBM类和收缩轨迹

IF 1.2 1区数学 Q1 MATHEMATICS

Algebraic Geometry Pub Date : 2019-07-30 DOI:10.14231/ag-2022-008

E. Amerik, M. Verbitsky

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引用次数: 2

摘要

超kahler流形上的MBM轨迹是具有负自交的最小有理曲线的所有变形的并集。MBM基因座可以等价地定义为双亚纯收缩的中心。证明了变形等价超kahler流形上的MBM轨迹是微分同胚的。我们使用对非代数K3曲面的Hilbert格式的变形来确定低维K3型hyperkahler流形上的MBM轨迹。

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MBM classes and contraction loci on low-dimensional hyperkähler manifolds of K3${}^{[n]}$ type

An MBM locus on a hyperkahler manifold is the union of all deformations of a minimal rational curve with negative self-intersection. MBM loci can be equivalently defined as centers of bimeromorphic contractions. It was shown that the MBM loci on deformation equivalent hyperkahler manifolds are diffeomorphic. We determine the MBM loci on a hyperkahler manifold of K3-type of low dimension using a deformation to a Hilbert scheme of a non-algebraic K3 surface.

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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.