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

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The recorded talks can be found at CIRGET channel : www.youtube.com/channel/UCLkFm-uEvXSf9y-iQtWOLWA