The non-archimedean SYZ fibration

Johannes Nicaise; Chenyang Xu; Tony Yue Yu

doi:10.1112/S0010437X19007152

The non-archimedean SYZ fibration

Johannes Nicaise, Chenyang Xu, Tony Yue Yu

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

We construct non-archimedean SYZ (Strominger-Yau-Zaslow) fibrations for maximally degenerate Calabi-Yau varieties, and we show that they are affinoid torus fibrations away from a codimension-two subset of the base. This confirms a prediction by Kontsevich and Soibelman. We also give an explicit description of the induced integral affine structure on the base of the SYZ fibration. Our main technical tool is a study of the structure of minimal dlt (divisorially log terminal) models along one-dimensional strata.

Original language	English (US)
Pages (from-to)	953-972
Number of pages	20
Journal	Compositio Mathematica
Volume	155
Issue number	5
DOIs	https://doi.org/10.1112/S0010437X19007152
State	Published - Jan 1 2019
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Strominger-Yau-Zaslow conjecture
minimal model program
mirror symmetry
non-archimedean geometry

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10.1112/S0010437X19007152

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title = "The non-archimedean SYZ fibration",

abstract = "We construct non-archimedean SYZ (Strominger-Yau-Zaslow) fibrations for maximally degenerate Calabi-Yau varieties, and we show that they are affinoid torus fibrations away from a codimension-two subset of the base. This confirms a prediction by Kontsevich and Soibelman. We also give an explicit description of the induced integral affine structure on the base of the SYZ fibration. Our main technical tool is a study of the structure of minimal dlt (divisorially log terminal) models along one-dimensional strata.",

keywords = "Strominger-Yau-Zaslow conjecture, minimal model program, mirror symmetry, non-archimedean geometry",

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T1 - The non-archimedean SYZ fibration

AU - Nicaise, Johannes

AU - Xu, Chenyang

AU - Yu, Tony Yue

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We construct non-archimedean SYZ (Strominger-Yau-Zaslow) fibrations for maximally degenerate Calabi-Yau varieties, and we show that they are affinoid torus fibrations away from a codimension-two subset of the base. This confirms a prediction by Kontsevich and Soibelman. We also give an explicit description of the induced integral affine structure on the base of the SYZ fibration. Our main technical tool is a study of the structure of minimal dlt (divisorially log terminal) models along one-dimensional strata.

AB - We construct non-archimedean SYZ (Strominger-Yau-Zaslow) fibrations for maximally degenerate Calabi-Yau varieties, and we show that they are affinoid torus fibrations away from a codimension-two subset of the base. This confirms a prediction by Kontsevich and Soibelman. We also give an explicit description of the induced integral affine structure on the base of the SYZ fibration. Our main technical tool is a study of the structure of minimal dlt (divisorially log terminal) models along one-dimensional strata.

KW - Strominger-Yau-Zaslow conjecture

KW - minimal model program

KW - mirror symmetry

KW - non-archimedean geometry

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VL - 155

SP - 953

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JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 5

ER -

The non-archimedean SYZ fibration

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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