A local Torelli theorem for log symplectic manifolds

Abstract: We will discuss how to deform a holomorphic symplectic form that has logarithmic poles along a normal crossings divisor. We will introduce an appropriate deformation complex and explain how to calculate its cohomology using natural local systems on the strata of the polar divisor. An analysis of the L-infinity structure on the cohomology of the deformation complex leads to a simple combinatorial description of the deformation space in terms of the periods of the log symplectic form. As an application, we construct new examples of log symplectic forms on $CP^4$ by deforming previously known ones. This is joint work with Brent Pym and Travis Schedler.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

[[Please provide your first and last name so that the speaker can identify you. Kindly submit your questions or comments using the chat box, not via audio.]]

The livestream is on Zoom at uqam.zoom.us/j/88383789249 It is recommended to subscribe to the CIRGET newsletter. Please send an email to haedrich.alexandra@uqam.ca , providing your name and affiliation.

Some talks can be seen at www.youtube.com/channel/UCLkFm-uEvXSf9y-iQtWOLWA