Scattering diagrams from blowups of toric surfaces

Abstract: Gross-Hacking-Keel has shown that any cluster variety can be obtained by a sequence of (nontoric) blow-ups and blow-downs starting from a toric variety. Motivated by this, we study the effect of blowup on the Lagrangian torus fibration on a toric surface. In particular, we will see that if the blowup points lie over the codimension one strata of the toric variety, the resulting fibration on the blowup produces a scattering diagram that matches with the one constructed by Gross-Pandharipande-Siebert using algebraic curve counting. The talk is based on the work in progress jointly with Sam Bardwell-Evans, Man-Wai Mandy Cheung and Yu-Shen Lin.

mathematical physicsalgebraic geometrysymplectic geometry

Audience: researchers in the topic

IBS-CGP weekly zoom seminar

Series comments: Registration is required at cgp.ibs.re.kr/activities/talkregistration