Constructing local models for Lagrangian torus fibrations

Evans, Jonathan David; Mauri, Mirko

doi:10.5802/ahl.80

Item

ITEM ACTIONSEXPORT

Add to Basket

Please note that a newer version of this item is available:
https://pure.mpg.de/pubman/item/item_3326677_3

DetailsSummary

Released

Journal Article

Constructing local models for Lagrangian torus fibrations

MPS-Authors

/persons/resource/persons262453

Mauri, Mirko
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.5802/ahl.80
(Publisher version)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

Evans-Mauri_Constructing local models for Lagrangian torus fibrations_2021.pdf
(Publisher version), 855KB

Supplementary Material (public)

There is no public supplementary material available

Citation

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

Cite as: https://hdl.handle.net/21.11116/0000-0008-BA0E-8

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. Then, 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.