Friday, March 29th, 2019
3:00pm - 4:00pm, in McCormack 1-210

Justin Sawon

UNC Chapel Hill

Lagrangian fibrations by Jacobians and Prym varieties

Abstract: A holomorphic fibration on a compact hyperkahler manifold must be Lagrangian, i.e., the fibers must be Lagrangian with respect to the holomorphic symplectic form and the general fiber must be an abelian variety. Hitchin integrable systems are non-compact Lagrangian fibrations; their fibers are Jacobians or Prym varieties of spectral curves. In this talk we explore compact analogues of Hitchin systems, i.e., compact Lagrangian fibrations by Jacobians and Prym varieties. We discuss how to construct examples, degenerations to Hitchin systems, and dual fibration relations between some of the examples.