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

doi:10.1007/s10473-023-0303-4

Abstract

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].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^*

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