Comptage de courbes sur le plan projectif \'eclat\'e en trois points align\'es

TL;DR

This paper proves a version of Manin's conjecture for a specific algebraic surface, the projective plane blown up at three collinear points, over a global field of positive characteristic.

Contribution

It establishes Manin's conjecture for a new class of algebraic surfaces in positive characteristic, extending previous results.

Findings

Verification of Manin's conjecture in this setting

Explicit counting of rational curves on the blown-up plane

New techniques for positive characteristic cases

Abstract

We prove a version of Manin's conjecture for the projective plane blown up in three collinear points, the base field being a global field of positive characteristic.