Elliptic fibrations on cubic surfaces
Gavin Brown, Daniel Ryder
TL;DR
This paper classifies elliptic fibrations on smooth cubic surfaces over characteristic zero fields, providing computational methods and an implementation for analyzing these fibrations.
Contribution
It offers a classification of elliptic fibrations on cubic surfaces and introduces computational techniques with a practical implementation.
Findings
Classification of elliptic fibrations on cubic surfaces
Development of computational analysis methods
Implementation in computer algebra systems
Abstract
We classify elliptic fibrations birational to a nonsingular, minimal cubic surface over a field of characteristic zero. Our proof is adapted to provide computational techniques for the analysis of such fibrations, and we describe an implementation of this analysis in computer algebra.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Finite Group Theory Research · Geometric and Algebraic Topology