Building Lagrangian Strominger-Yau-Zaslow fibrations II
Organizers
Speaker
Illia Zharkov
Time
Wednesday, June 4, 2025 3:00 PM - 4:30 PM
Venue
A7-201
Online
Zoom 204 323 0165
(BIMSA)
Abstract
Given an integral affine manifold $B$ with (semi-)simple singularities $D$ in codimension $2$, I will explain a strategy how to build a symplectic manifold $X$ and the Lagrangian torus fibration $X \to B$ which extends the tautological cotangent torus bundle over $B\backslash D$. As an example, I will take the anti-canonical hypersurface in a Fano toric variety. The main emphasis of the second (more technical) lecture will be on how to inductively use the Liouville flow cone tool of Evans-Mauri to build the torus fibration from the Liouville boundary. I will focus on the local model $x..z=1+w_1+...+w_n$. If time permits I will explain what one can say about the topology of the singular fiber. This is a joint project with C-Y. Mak, D. Matessi and H. Ruddat.