A Local Torelli Theorem for Log Symplectic Manifolds

Explore a comprehensive lecture on log symplectic manifolds and their local Torelli theorem. Delve into the generalization of holomorphic symplectic manifolds, where symplectic forms develop mild poles on hypersurfaces. Discover the local model for the moduli space of log symplectic manifolds, focusing on those with normal crossing degeneracy divisors. Compare the similarities and differences with the local Torelli theorem for compact holomorphic symplectic manifolds, examining how the moduli space is described through second cohomology. Investigate the highly singular and reducible nature of the log symplectic case, understanding the impact of deforming hypersurface singularities under specific integrality constraints. Learn about the application of these methods in producing new irreducible components of the moduli space of log symplectic structures on Pn. This lecture, presented by Brent Pym at the Hausdorff Center for Mathematics, is based on joint work with Mykola Matviichuk and Travis Schedler.