Rational Points on Del Pezzo Surface of degree 1 and 2
Shuijing Li
TL;DR
This paper investigates the distribution and explicit equations of rational points on del Pezzo surfaces of degrees 1 and 2 over finite fields, providing new insights into their structure and unique rational points.
Contribution
It offers explicit equations for del Pezzo surfaces with a unique rational point and analyzes rational points over finite fields, advancing understanding of these surfaces.
Findings
Explicit equations for del Pezzo surfaces with a unique rational point
Characterization of rational points on degree 1 and 2 del Pezzo surfaces over finite fields
Identification of conditions for the existence of a unique rational point
Abstract
We discuss the rational points on del Pezzo surface of degree 1 and 2 over any finite field , and give out the explicit equations of del Pezzo surfaces that have unique rational point.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems · Polynomial and algebraic computation