Elliptic surfaces and toroidal superalgebras

The equivariant cohomology of certain moduli spaces of sheaves on isotrivial elliptic surfaces are shown to admit representations of infinite dimensional Lie (super)algebras. The construction is based on work of Billig and Chen-Li-Tan on vertex representations of toroidal extended affine Lie algebras, and a geometric interpretation of bc-ghost systems on Hilbert schemes of points on ruled surfaces. The role of higher-nullity toroidal extended affine lie algebras are discussed in relation to tensor products of modules of a Yangian-like associative algebra. Applications to enumerative geometry are discussed in the introduction.