Brane quantization of A_n-resolutions

2026/06/23 by Yat-Hin Suen, Yutung Yau · 1 voice
#math.SG #math-ph #math.AG #math.DG #math.MP

paper · pdf

Abstract

We extend the study of brane quantization via SYZ mirror symmetry to the setting of singular fibers, building on recent joint work with Chan, Leung, and Li in the semi-flat case. We consider a crepant resolution X→ℂ²/ℤ_n+1 of the A_n-singularity, whose mirror \checkX is also realized as a resolution of ℂ²/ℤ_n+1. For each level k∈ℤ_>0, we construct a space filling coisotropic A-brane B_cc^(k) of (X,kω) and determine its mirror B-brane \checkB_cc^(k) via fiberwise geometric quantization. We then define the endomorphism algebra Hom_A(B_cc^(k),B_cc^(k)) by gluing analytic quantum tori using wall-crossing formulas and establish a mirror isomorphism Hom_A(B_cc^(k),B_cc^(k))≅ Hom_B(\checkB_cc^(k),\checkB_cc^(k)).

Discussions

• Yat-Hin Suen, Yutung Yau: Brane quantization of $A_n$-resolutions https://arxiv.org/abs/2606.24249 https://arxiv.org/pdf/2606.24249 https://arxiv.org/html/2606.24249 [bsky, 0 points, 0 comments]

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