On the moduli of surfaces admitting genus two fibrations over elliptic curves

DOI10.1007/S00013-007-2139-XzbMATH Open1155.14011arXivmath/0608489OpenAlexW1977771523MaRDI QIDQ2474109

Author name not available (Why is that?)

Publication date: 5 March 2008

Published in: (Search for Journal in Brave)

Abstract: In this paper, we study the structure, deformations and the moduli spaces of complex projective surfaces admitting genus two fibrations over elliptic curves. We observe that, a surface admitting a smooth fibration as above is elliptic and we employ results on the moduli of polarized elliptic surfaces, to construct moduli spaces of these smooth fibrations. In the case of nonsmooth fibrations, we relate the moduli spaces to the Hurwitz schemes $calH(1,X(d),n)$ of morphisms of degree $n$ from elliptic curves to the modular curve $X(d)$, $dgeq3$. Ultimately, we show that the moduli spaces in the nonsmooth case are fiber spaces over the affine line ${mathbbA}^1$ with fibers determined by the components of $calH(1,X(d),n)$.

Full work available at URL: https://arxiv.org/abs/math/0608489

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: On the moduli of surfaces admitting genus two fibrations over elliptic curves

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2474109)