3 papers
math.NT2026
Quartic del Pezzo surfaces over without quadratic points
Giorgio Navone, Katerina Santicola, Harry C. Shaw +1
We construct an infinite family of quartic del Pezzo surfaces over with no quadratic points, for all primes . This answers a question of Colliot--Thélène…
math.NT2025
Stability of the Kato-Kuzumaki's properties under field extensions
Felipe Gambardella, Harry C. Shaw
In 1986, Kato and Kuzumaki introduced some Diophantine properties of fields, called the properties, and they hoped they would provide a good characterization of the cohomol…
math.AG2024
Diagonal del Pezzo of degree 2 with a Brauer-Manin obstruction
Harry C. Shaw
In this paper we give an asymptotic formula for the quantity of diagonal del Pezzo surfaces of degree 2 which have a Brauer-Manin obstruction to the Hasse principle when ordered by…