Birational automorphism groups in families of hyper-K\"ahler manifolds

TL;DR

This paper investigates how the groups of birational automorphisms vary within families of projective hyper-K"ahler manifolds, providing insights into their structural behavior.

Contribution

It offers new understanding of the dynamics of birational automorphism groups in hyper-K"ahler families, a topic with limited prior exploration.

Findings

Analysis of automorphism group behavior in hyper-K"ahler families

Identification of conditions affecting group variation

Insights into the structure of automorphism groups in algebraic geometry

Abstract

We study the behavior of birational automorphism groups in families of projective hyper-K\"ahler manifolds.