Splitting Varieties for Cup Products with $\mathbb Z/3$-Coefficients

TL;DR

This paper introduces a new method linking Veronese embeddings to splitting varieties of cup products, providing an algorithm for their construction with explicit results for n=3, and applying it to Galois group realization.

Contribution

It presents a novel algorithm for constructing splitting varieties for cup products with Z/n coefficients, including explicit calculations for n=3, and connects these to Galois theory.

Findings

Algorithm for constructing splitting varieties for Z/n cup products

Explicit calculation of splitting varieties for n=3

Application to Galois group realization

Abstract

We connect Veronese embeddings to splitting varieties of cup products. We then give an algorithm for constructing splitting varieties for cup products with $\mathbb Z/n$ coefficients, with an explicit calculation for $n=3$. An application to the automatic realization of Galois groups is given.