Singular Log Structures and Log Crepant Log Resolutions I

Name: Singular Log Structures and Log Crepant Log Resolutions I
Keywords: Mathematics - Algebraic Geometry, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 14A21, 14B05, 14M25, 14E15, 14J33, 14J45, Algebraic Geometry (math.AG)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2025Embargo end date: 01 Jan 2025Publisher:arXiv

Authors: Corti, Alessio; Graefnitz, Tim; Ruddat, Helge;

doi: 10.48550/arxiv.2503.11610

arXiv: http://arxiv.org/abs/2503.11610

Singular Log Structures and Log Crepant Log Resolutions I

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Abstract

We introduce a class of singular log schemes in three dimensions and conjecture that log schemes in this class admit log crepant log resolutions. We provide examples as evidence and relate this conjecture to the conjecture made in [4] and the Gross--Siebert program.

15 pages, 6 figures

Keywords

Mathematics - Algebraic Geometry, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 14A21, 14B05, 14M25, 14E15, 14J33, 14J45, Algebraic Geometry (math.AG)

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