La conjecture de Manin g\'eom\'etrique pour une famille de quadriques intrins\`eques

TL;DR

This paper proves a version of Manin's conjecture for a family of intrinsic quadrics over global fields of positive characteristic, and extends the method to certain generalized del Pezzo surfaces.

Contribution

It introduces a novel approach to verify Manin's conjecture for intrinsic quadrics and related surfaces in positive characteristic settings.

Findings

Proves Manin's conjecture for intrinsic quadrics over positive characteristic fields.

Extends the method to generalized del Pezzo surfaces with slight modifications.

Provides a framework applicable to other algebraic varieties in similar contexts.

Abstract

We prove a version of Manin's conjecture for a certain family of intrinsic quadrics, the base field being a global field of positive characteristic. We also explain how a very slight variation of the method we use allows to establish the conjecture for a certain generalized del Pezzo surface.