Counting rational points on del Pezzo surfaces with a conic bundle structure
T.D. Browning, M. Swarbrick Jones
TL;DR
This paper establishes upper bounds for the number of rational points of bounded height on non-singular del Pezzo surfaces over any number field, focusing on those with conic bundle structures.
Contribution
It provides new upper bounds for rational points on del Pezzo surfaces with conic bundle structures over arbitrary number fields.
Findings
Upper bounds for rational points established
Applicable to non-singular del Pezzo surfaces over any number field
Focus on surfaces with conic bundle structures
Abstract
For any number field k, upper bounds are established for the number of k-rational points of bounded height on non-singular del Pezzo surfaces defined over k, which are equipped with suitable conic bundle structures over k.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Tensor decomposition and applications · Polynomial and algebraic computation