On Hirzebruch invariants of elliptic fibrations

James Fullwood, Mark van Hoeij

We compute all Hirzebruch invariants chi_q for D5, E6, E7 and E8 elliptic fibrations of every dimension. A single generating series chi(t,y) is produced for each family of fibrations such that the coefficient of t^ky^q encodes chi_q over a base of dimension k, solely in terms of invariants of the base of the fibration.