Gianluca Pacienza (University of Lorraine and CNRS, Nancy)

Title: Deformations of rational curves on primitive symplectic varieties and applications

Abstract: 
I will present a joint work with Ch. Lehn and G. Mongardi in which we study the deformation 
theory of rational curves on a (possibly singular) primitive symplectic variety X and show 
that if the rational curves cover a divisor, then, as in the smooth case, they deform along 
their Hodge locus.
As applications, we extend Markman's deformation invariance of prime exceptional divisors to 
this singular framework and provide existence results for uniruled ample divisors on primitive 
symplectic varieties which are locally trivial deformation of any moduli space of sheaves on a 
projective K3 or fibers of the Albanese map of those on an abelian surface.