On Gauss-Bonnet and Poincaré-Hopf type theorems for complex ∂-manifolds

2018/08/15 by Corrêa, Maurício, Lourenço, Fernando, Machado, Diogo +1
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.05178

Abstract

We prove a Gauss-Bonnet and Poincaré-Hopf type theorems for complex ∂-manifold X = X - D, where X is a complex compact manifold and D is a reduced divisor. We will consider the cases such that D has isolated singularities and also if D has a (not necessarily irreducible) decomposition D=D₁∪ D₂ such that D₁, D₂ have isolated singularities and C=D₁∩ D₂ is a codimension 2 variety with isolated singularities.

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