On the genus of elliptic fibrations

Gatsinzi, J.-B.

doi:10.1090/S0002-9939-03-07203-4

On the genus of elliptic fibrations
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Proc. Amer. Math. Soc. 132 (2004), 597-606 Request permission

Abstract:

A simply connected topological space is called elliptic if both $\pi _*(X, \mathbb {Q})$ and $H^*(X, \mathbb {Q})$ are finite-dimensional $\mathbb {Q}$-vector spaces. In this paper, we consider fibrations for which the fibre $X$ is elliptic and $H^*(X, \mathbb {Q})$ is evenly graded. We show that in the generic cases, the genus of such a fibration is completely determined by generalized Chern classes of the fibration.

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