2021/04/06 by Valentin Lychagin, Lychagin, Valentin, Mikhail Roop +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2104.02376
openalex publication_date 2021/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In these lectures, we discuss two approaches to studying orbit spaces of algebraic Lie groups. Due to algebraic approach orbit space, or quotient, is an algebraic manifold, while from the differential viewpoint a quotient is a differential equation. The main goal of these lectures is to show that the differential approach gives us a better understanding of structure of invariants and orbit spaces. We illustrate this on classical equivalence problems, such as SL - classification of binary and ternary forms, and affine classification of algebraic plane curves.