Algebraic magnetism invariants of a double scalar action on the projective plane

2025/09/04 by Arnaud Mayeux, Mayeux, Arnaud
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2509.04274

openalex publication_date 2025/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

This document is an expanded version of the notes from a talk at the Arithmetic and Algebraic Geometry Week conference, which took place in Iasi in September 2025. In this note, we compute the pure magnets (certain semigroups) and the associated attractors for a double scalar action of \mathbbG_m² on ℙ². This is mostly expository and provides a non-affine example illustrating the invariants of Algebraic Magnetism in a simple and visual case. Nevertheless, we introduce the notion of lambdafiable magnets, in the general setting, to relate certain magnets to cocharacters. Finally we announce recent advanced results on Algebraic Magnetism obtained in \citeBM and solving positively some conjectures stated in \citeMa.

Citations

• Algebraic Magnetism Invariants of Self-Actions of Diagonalizable Monoid Schemes
• Moduli spaces and geometric invariant theory: old and new perspectives
• Białynicki-Birula decomposition for reductive groups

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