Triple Massey products for higher genus curves

TL;DR

This paper investigates the conditions under which triple Massey products vanish for higher genus curves over number fields, providing explicit examples of hyperelliptic curves with non-vanishing Massey products.

Contribution

It constructs explicit hyperelliptic curves of genus greater than one with non-vanishing triple Massey products over certain primes, advancing understanding of their behavior in algebraic geometry.

Findings

Existence of hyperelliptic curves with non-zero triple Massey products

Construction of examples for all genus g > 1 and primes l > 3

Insight into the non-vanishing phenomenon of Massey products in higher genus curves

Abstract

We study the vanishing of triple Massey products for absolutely irreducible smooth projective curves over a number field. For each genus $g > 1$ and each prime $\ell > 3$, we construct examples of hyperelliptic curves of genus $g$ for which there are non-empty triple Massey products with coefficients in $\mathbb{Z}/\ell$ that do not contain $0$.