Building Lagrangian Strominger-Yau-Zaslow fibrations II
演讲者
Illia Zharkov
时间
2025年06月04日 15:00 至 16:30
地点
A7-201
线上
Zoom 204 323 0165
(BIMSA)
摘要
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.