On equivariant indices of 1-forms on varieties

2017/01/07 by S. M. Gusein‐Zade, Gusein-Zade, Sabir M., Firuza I. Mamedova +1
Mathematics · #14B05 #19A22 #58A10 #58E40 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1701.01827

openalex publication_date 2017/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a G-invariant holomorphic 1-form with an isolated singular point on a germ of a complex-analytic G-variety with an isolated singular point (G is a finite group) one has notions of the equivariant homological index and of the (reduced) equivariant radial index as elements of the ring of complex representations of the group. We show that on a germ of a smooth complex-analytic G-variety these indices coincide. This permits to consider the difference between them as a version of the equivariant Milnor number of a germ a G-variety with an isolated singular point.

Related

• Homological index for 1-forms and a Milnor number for isolated singularities
• Equivariant indices of vector fields and 1-forms
• Indices of collections of equivariant 1-forms and characteristic numbers
• Proportionality of Indices of 1-Forms on Singular Varieties
• Indices of 1-forms on an isolated complete intersection singularity