Constructing local models for Lagrangian torus fibrations

Autor:	Evans, Jonathan David, Mauri, Mirko
Rok vydání:	2019
Předmět:	Mathematics - Symplectic Geometry Mathematics - Algebraic Geometry 53D37 (Primary) 53D35 14J33 14G22 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 38 pages, 14 figures; minor changes, to appear in AHL
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1905.09229 Zobrazit plný text záznamu View this record from Arxiv