On the Invariant Theory of Unipotent Groups Actions from a Geometric Perspective

Puntos clave

• Open $G$-stable affine sub-varieties can either form trivial bundles or exhibit more complex structures, with implications for topology.
• The study introduces an $\alpha$-pair concept that defines specific bundle conditions over $G$-actions in connected unipotent groups.
• Generalizations of van den Essen's algorithm are explored for quasi-principle $G$-varieties, contributing to geometric invariant theory.
• Connections between Zariski and fppf topologies influence the classification of variations in group actions on varieties.

Resumen