Vector Bundles over Elliptic Fibrations

TL;DR

This paper develops methods for constructing vector bundles over elliptic curves and their families, including universal families, with detailed examples and Chern class calculations.

Contribution

It introduces new constructions of vector bundles over elliptic fibrations, including spectral cover and extension methods, with a focus on universal families and relative versions.

Findings

Constructed universal families over generalized elliptic curves.

Provided explicit examples and Chern class computations.

Developed relative construction methods for families of elliptic curves.

Abstract

This paper gives various methods for constructing vector bundles over elliptic curves and more generally over families of elliptic curves. We construct universal families over generalized elliptic curves via spectral cover methods and also by extensions, and then give a relative version of the construction in families. We give various examples and make Chern class computations.