A family of K3 surfaces and towers of algebraic curves over finite fields

TL;DR

This paper constructs a new family of algebraic curves over finite fields using K3 surfaces, resulting in a tower that is optimal for certain primes, advancing the understanding of algebraic geometry over finite fields.

Contribution

It introduces a novel construction of towers of algebraic curves over finite fields based on a family of K3 surfaces, extending previous methods.

Findings

Achieved a good tower over =_{p^2}

The tower is optimal when p=3

Provides a new geometric approach to constructing algebraic curve towers

Abstract

For a family of K3 surfaces we implement a variation of a general construction of towers of algebraic curves over finite fields given in a previous paper. As a result we get a good tower over $k=\mathbb{F}_{p^2}$, that is optimal if $p=3$.