STABILITY CONDITIONS AND THE MIRROR SYMMETRY OF K3 SURFACES IN ATTRACTOR BACKGROUNDS*

doi:10.1007/s10473-023-0303-4

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (3): 1007-1030.doi: 10.1007/s10473-023-0303-4

STABILITY CONDITIONS AND THE MIRROR SYMMETRY OF K3 SURFACES IN ATTRACTOR BACKGROUNDS^*

Wenxuan Lu

School of Mathematics and Statistics, Yunnan University, Kunming 650091, China

收稿日期:2021-09-16 修回日期:2022-10-23 出版日期:2023-06-25 发布日期:2023-06-06
作者简介:Wenxuan Lu, E-mail: wenxuanlu@ynu.edu.cn

STABILITY CONDITIONS AND THE MIRROR SYMMETRY OF K3 SURFACES IN ATTRACTOR BACKGROUNDS^*

Wenxuan Lu

School of Mathematics and Statistics, Yunnan University, Kunming 650091, China

Received:2021-09-16 Revised:2022-10-23 Online:2023-06-25 Published:2023-06-06
About author:Wenxuan Lu, E-mail: wenxuanlu@ynu.edu.cn

摘要/Abstract

摘要： We study the space of stability conditions on $K3$ surfaces from the perspective of mirror symmetry. This is done in the attractor backgrounds (moduli). We find certain highly non-generic behaviors of marginal stability walls (a key notion in the study of wall crossings) in the space of stability conditions. These correspond via mirror symmetry to some non-generic behaviors of special Lagrangians in an attractor background. The main results can be understood as a mirror correspondence in a synthesis of the homological mirror conjecture and SYZ mirror conjecture.

关键词: mirror symmetry, stability conditions, $K3$ surfaces, attractor mechanism

Abstract: We study the space of stability conditions on $K3$ surfaces from the perspective of mirror symmetry. This is done in the attractor backgrounds (moduli). We find certain highly non-generic behaviors of marginal stability walls (a key notion in the study of wall crossings) in the space of stability conditions. These correspond via mirror symmetry to some non-generic behaviors of special Lagrangians in an attractor background. The main results can be understood as a mirror correspondence in a synthesis of the homological mirror conjecture and SYZ mirror conjecture.

Key words: mirror symmetry, stability conditions, $K3$ surfaces, attractor mechanism

Wenxuan Lu. STABILITY CONDITIONS AND THE MIRROR SYMMETRY OF K3 SURFACES IN ATTRACTOR BACKGROUNDS^*[J]. 数学物理学报(英文版), 2023, 43(3): 1007-1030.

Wenxuan Lu. STABILITY CONDITIONS AND THE MIRROR SYMMETRY OF K3 SURFACES IN ATTRACTOR BACKGROUNDS^*[J]. Acta mathematica scientia,Series B, 2023, 43(3): 1007-1030.

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STABILITY CONDITIONS AND THE MIRROR SYMMETRY OF K3 SURFACES IN ATTRACTOR BACKGROUNDS^*

STABILITY CONDITIONS AND THE MIRROR SYMMETRY OF K3 SURFACES IN ATTRACTOR BACKGROUNDS^*

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