Index theorems for couples of holomorphic self-maps

2016/04/06 by P Arcangeli, Arcangeli, Paolo
Mathematics · #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1604.01569

openalex publication_date 2016/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a n-dimensional complex manifold and f,g:M→ M two distinct holomorphic self-maps. Suppose that f and g coincide on a globally irreducible compact hypersurface S⊂ M. We show that if one of the two maps is a local biholomorphism around S'=S-Sing(S) and, if needed, S' sits into M in a particular nice way, then it is possible to define a 1-dimensional holomorphic (possibly singular) foliation on S' and partial holomorphic connections on certain holomorphic vector bundles on S'. As a consequence, we are able to localize suitable characteristic classes and thus to get index theorems.

Related

• Index theorems for holomorphic self-maps
• Index theorems for holomorphic maps and foliations
• Index theorems for meromorphic self-maps of the projective space
• Heat kernel and local index theorem for open complex manifolds with ℂ^∗ -action
• Indices of holomorphic foliations and the bifurcation conjecture