Let be an elliptic spectrum with elliptic curve . We show that the sigma orientation of Ando, Hopkins and Strickland [Invent. Math 146 (2001) 595-687] and Hopkins [Proceedings of the ICM 1-2 (1995) 554-565] gives rise to a genus of SU–manifolds taking its values in meromorphic functions on . As varies we find that the genus is a meromorphic arithmetic Jacobi form. When is the Tate elliptic curve it specializes to the two-variable elliptic genus studied by many. We also show that this two-variable genus arises as an instance of the –equivariant sigma orientation.
"The Jacobi orientation and the two-variable elliptic genus." Algebr. Geom. Topol. 8 (1) 493 - 539, 2008. https://doi.org/10.2140/agt.2008.8.493