# A uniform bound on the Brauer groups of certain log K3 surfaces

## TL;DR

This paper establishes a uniform bound on the size of the Brauer group for certain log K3 surfaces, specifically complements of smooth anticanonical divisors in del Pezzo surfaces of degree ≤7 over number fields.

## Contribution

It provides the first effective uniform bound on the Brauer groups of these specific log K3 surfaces, linking the bound to the degree of the base number field.

## Key findings

- Effective uniform bound for Brauer groups established
- Bound depends explicitly on the degree of the number field
- Advances understanding of arithmetic properties of log K3 surfaces

## Abstract

Let U be the complement of a smooth anticanonical divisor in a del Pezzo surface of degree at most 7 over a number field k. We show that there is an effective uniform bound for the size of the Brauer group of U in terms of the degree of k.