An elementary description of nef cone for irreducible holomorphic symplectic manifolds

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-10-29 DOI:10.1016/j.geomphys.2024.105349

Anastasia V. Vikulova

引用次数: 0

Abstract

We describe MBM classes for irreducible holomorphic symplectic manifolds of K3 and Kummer types. These classes are the monodromy images of extremal rational curves which give the faces of the nef cone of some birational model. We study the connection between our results and A. Bayer and E. Macrì's theory. We apply the numerical method of description due to E. Amerik and M. Verbitsky in low dimensions to the K3 type and Kummer type cases.

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不可还原全态交映流形内锥的基本描述

我们描述了 K3 和 Kummer 型不可还原全形交映流形的 MBM 类。这些类是极值有理曲线的单旋转图像，它们给出了某个双向模型的内锥面。我们研究了我们的结果与 A. Bayer 和 E. Macrì 的理论之间的联系。我们将 E. Amerik 和 M. Verbitsky 提出的低维数值描述方法应用于 K3 型和 Kummer 型情况。

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

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity