Extremal rational elliptic threefolds
A. Prendergast-Smith
TL;DR
This paper classifies specific nets of quadrics in projective 3-space that produce elliptic fibrations with Mordell-Weil rank zero, advancing understanding of elliptic threefolds.
Contribution
It provides a classification of nets of quadrics in P^3 leading to elliptic fibrations with Mordell-Weil rank zero, a novel contribution in algebraic geometry.
Findings
Complete classification of relevant nets of quadrics
Identification of conditions for Mordell-Weil rank zero
Insights into the structure of extremal elliptic threefolds
Abstract
We classify nets of quadrics in P^3 which give rise to elliptic fibrations of Mordell-Weil rank zero.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometric and Algebraic Topology