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Constructing local models for Lagrangian torus fibrations

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Constructing local models for Lagrangian torus fibrations. / Evans, Jonny; Mauri, Mirko.
In: Annales Henri Lebesgue, Vol. 4, 30.01.2021, p. 537-570.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Evans, J & Mauri, M 2021, 'Constructing local models for Lagrangian torus fibrations', Annales Henri Lebesgue, vol. 4, pp. 537-570. https://doi.org/10.5802/ahl.80

APA

Evans, J., & Mauri, M. (2021). Constructing local models for Lagrangian torus fibrations. Annales Henri Lebesgue, 4, 537-570. https://doi.org/10.5802/ahl.80

Vancouver

Evans J, Mauri M. Constructing local models for Lagrangian torus fibrations. Annales Henri Lebesgue. 2021 Jan 30;4:537-570. doi: 10.5802/ahl.80

Author

Evans, Jonny ; Mauri, Mirko. / Constructing local models for Lagrangian torus fibrations. In: Annales Henri Lebesgue. 2021 ; Vol. 4. pp. 537-570.

Bibtex

@article{6e99e7403abd42f596d16064ecef3ab5,
title = "Constructing local models for Lagrangian torus fibrations",
abstract = "We give a construction of Lagrangian torus fibrations with controlled discriminant locus on certain affine varieties. In particular, we apply our construction in the following ways: > We find a Lagrangian torus fibration on the 3-fold negative vertex whose discriminant locus has codimension 2; this provides a local model for finding torus fibrations on compact Calabi–Yau 3-folds with codimension 2 discriminant locus. > We find a Lagrangian torus fibration on a neighbourhood of the one-dimensional stratum of a simple normal crossing divisor (satisfying certain conditions) such that the base of the fibration is an open subset of the cone over the dual complex of the divisor. This can be used to construct an analogue of the non-archimedean SYZ fibration constructed by Nicaise, Xu and Yu.",
keywords = "Lagrangian torus, SYZ fibration, dual complex, negative vertex",
author = "Jonny Evans and Mirko Mauri",
year = "2021",
month = jan,
day = "30",
doi = "10.5802/ahl.80",
language = "English",
volume = "4",
pages = "537--570",
journal = "Annales Henri Lebesgue",
issn = "2644-9463",
publisher = "{\'E}cole normale sup{\'e}rieure de Rennes",

}

RIS

TY - JOUR

T1 - Constructing local models for Lagrangian torus fibrations

AU - Evans, Jonny

AU - Mauri, Mirko

PY - 2021/1/30

Y1 - 2021/1/30

N2 - We give a construction of Lagrangian torus fibrations with controlled discriminant locus on certain affine varieties. In particular, we apply our construction in the following ways: > We find a Lagrangian torus fibration on the 3-fold negative vertex whose discriminant locus has codimension 2; this provides a local model for finding torus fibrations on compact Calabi–Yau 3-folds with codimension 2 discriminant locus. > We find a Lagrangian torus fibration on a neighbourhood of the one-dimensional stratum of a simple normal crossing divisor (satisfying certain conditions) such that the base of the fibration is an open subset of the cone over the dual complex of the divisor. This can be used to construct an analogue of the non-archimedean SYZ fibration constructed by Nicaise, Xu and Yu.

AB - We give a construction of Lagrangian torus fibrations with controlled discriminant locus on certain affine varieties. In particular, we apply our construction in the following ways: > We find a Lagrangian torus fibration on the 3-fold negative vertex whose discriminant locus has codimension 2; this provides a local model for finding torus fibrations on compact Calabi–Yau 3-folds with codimension 2 discriminant locus. > We find a Lagrangian torus fibration on a neighbourhood of the one-dimensional stratum of a simple normal crossing divisor (satisfying certain conditions) such that the base of the fibration is an open subset of the cone over the dual complex of the divisor. This can be used to construct an analogue of the non-archimedean SYZ fibration constructed by Nicaise, Xu and Yu.

KW - Lagrangian torus

KW - SYZ fibration

KW - dual complex

KW - negative vertex

U2 - 10.5802/ahl.80

DO - 10.5802/ahl.80

M3 - Journal article

VL - 4

SP - 537

EP - 570

JO - Annales Henri Lebesgue

JF - Annales Henri Lebesgue

SN - 2644-9463

ER -