David Bai (Yale): Theorem of the square and fibrations of Hilbert schemes

On the Jacobian of a curve, the Fourier-Mukai autoequivalence of its derived category satisfies a symmetry known as theorem of the square, which roughly is its compatibility with the group structure on the Jacobian given by tensor product. The analogue of this suite of properties (group action, Fourier-Mukai transform, theorem of the square) is generally missing for a generically abelian fibration, except for the known cases of compactified Jacobians. In this talk, I’ll discuss these properties for another class of generically abelian fibrations: Hilbert schemes of points on elliptic surfaces.