This article is cited in 1 paper

On Gauss–Bonnet and Poincaré–Hopf type theorems for complex $\partial$-manifolds

Maurício Corrêa^a, Fernando Lourenço^b, Diogo Machado^c, Antonio M. Ferreira<sup>b

a</sup> Icex – UFMG, Av. Antônio Carlos 6627, 30123-970, Belo Horizonte-MG, Brazil
^b DEX – UFLA, Campus Universitário, Lavras MG, Brazil, CEP 37200-000
^c DMA – UFV, Avenida Peter Henry Rolfs, s/n – Campus Universitário, 36570-900 Vi cosa-MG, Brazil

Abstract: We prove a Gauss–Bonnet and Poincaré–Hopf type theorem for complex $\partial$-manifold $\widetilde{X} = X - D$, 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 $D=D_1\cup D_2$ such that $D_1$, $D_2$ have isolated singularities and $C=D_1\cap D_2$ is a codimension $2$ variety with isolated singularities.

Key words and phrases: logarithmic foliations, Gauss–Bonnet type theorem, Poincaré–Hopf index, residues.

MSC: 32S65, 32S25, 14C17

Language: English

DOI: 10.17323/1609-4514-2021-21-3-493-506

Bibliographic databases:

•