Families of embeddings of the alternating group of rank 5 into the Cremona group

TL;DR

This paper classifies and analyzes various embeddings of the alternating group A_5 into the Cremona group of rank three, revealing continuous families of non-conjugate embeddings.

Contribution

It provides a complete classification of embeddings induced by A_5-del Pezzo fibrations and demonstrates the existence of continuous families of non-conjugate embeddings.

Findings

All embeddings induced by A_5-del Pezzo fibrations are classified.

Existence of continuous families of pairwise non-conjugate embeddings.

Insights into the conjugacy classes of these embeddings within the Cremona group.

Abstract

I study embeddings of alternating group of rank five into the Cremona group of rank three. I find all embeddings induced by A_5-del Pezzo fibrations and I study their conjugacy. As an application, I show that there is a series of continuous families of pairwise non-conjugate embeddings of alternating group of rank five into Cr$_3(\mathbb{C})$.