Mirror partner for a Klein quartic polynomial

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-05-20 DOI:10.1016/j.geomphys.2025.105538

Alexey Basalaev

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引用次数: 0

Abstract

The results of A. Chiodo, Y. Ruan and M. Krawitz associate the mirror partner Calabi–Yau variety X to a Landau–Ginzburg orbifold

(f, G)

if f is an invertible polynomial satisfying Calabi–Yau condition and the group G is a diagonal symmetry group of f. In this paper we investigate the Landau–Ginzburg orbifolds with a Klein quartic polynomial

f = x_{1}^{3} x_{2} + x_{2}^{3} x_{3} + x_{3}^{3} x_{1}

and G being all possible subgroups of

GL (3, C)

, preserving the polynomial f and also the pairing in its Jacobian algebra. In particular, G is not necessarily abelian or diagonal. The zero–set of polynomial f, called Klein quartic, is a genus 3 smooth compact Riemann surface. We show that its mirror Landau–Ginzburg orbifold is

(f, G)

with G being a

Z / 2 Z

–extension of a Klein four–group.

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Klein四次多项式的镜像伙伴

结果a . Chiodo y阮副镜子和m . Krawitz伙伴比丘各种X Landau-Ginzburg orbifold (f, G)如果f是一个可逆的多项式满足比丘条件和f的G组是一个对角线对称群。在本文中,我们探讨Landau-Ginzburg orbifolds与克莱因四次多项式f = x13x2 + x23x3 + x33x1和G的所有可能的子组GL (3 C),保存多项式f和雅可比矩阵代数的配对。特别地，G不一定是阿贝尔的或对角的。多项式f的零集称为克莱因四次，是一个3属光滑紧致黎曼曲面。我们证明了它的镜像Landau-Ginzburg轨道是（f，G），其中G是Klein四群的Z/ 2z扩展。

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