Constructing local models for Lagrangian torus fibrations

Evans, Jonny and Mauri, Mirko (2021) Constructing local models for Lagrangian torus fibrations. Annales Henri Lebesgue, 4. pp. 537-570. ISSN 2644-9463

[thumbnail of em]
Text (em)
em.pdf - Accepted Version
Available under License Unspecified.

Download (873kB)


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.

Item Type:
Journal Article
Journal or Publication Title:
Annales Henri Lebesgue
?? lagrangian torussyz fibrationdual complexnegative vertex ??
ID Code:
Deposited By:
Deposited On:
13 Aug 2020 15:10
Last Modified:
08 May 2024 15:45