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Yat-Hin, Suen
기하학 수리물리 연구단
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Tropical Lagrangian multi-sections and smoothing of locally free sheaves over degenerate Calabi-Yau surfaces

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Title
Tropical Lagrangian multi-sections and smoothing of locally free sheaves over degenerate Calabi-Yau surfaces
Author(s)
Chan, Kwokwai; Ma, Ziming Nikolas; Yat-Hin Suen
Publication Date
2022-06
Journal
Advances in Mathematics, v.401
Publisher
Academic Press Inc.
Abstract
© 2022 Elsevier Inc.We introduce the notion of tropical Lagrangian multi-sections over a 2-dimensional integral affine manifold B with singularities, and use them to study the reconstruction problem for higher rank locally free sheaves over Calabi-Yau surfaces. To certain tropical Lagrangian multi-sections L over B, which are explicitly constructed by prescribing local models around the ramification points, we construct locally free sheaves E0(L,ks) over the singular projective scheme X0(B,P,s) associated to B equipped with a polyhedral decomposition P and a gluing data s. We then find combinatorial conditions on such an L under which the sheaf E0(L,ks) is simple. This produces explicit examples of smoothable pairs (X0(B,P,s),E0(L,ks)) in dimension 2.
URI
https://pr.ibs.re.kr/handle/8788114/11974
DOI
10.1016/j.aim.2022.108280
ISSN
0001-8708
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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