Residue Formulas for logarithmic Foliations and applications

Abstract

In this work we prove a Baum-Bott type formula for non-compact complex manifold of the form $\tilde{X}=X-\mathcal{D}$, where $X$ is a complex compact manifold and $\mathcal{D}$ is a normal crossing divisor on $X$. As applications, we provide a Poincaré-Hopf type Theorem and an optimal description for a smooth hypersurface $\mathcal{D}$ invariant by an one-dimensional foliation $\mathcal{F}$ on ${\mathbb{P}}^n$ satisfying $Sing(\mathcal{F})⊊\mathcal{D}.$

arXiv comment20 pages, to appear in Transactions of the American Mathematical Society. Major changes following suggestions of the referees

References in corpus (4)

• Chern classes for singular hypersurfaces
• On a conjecture of Varchenko
• Poincaré problem for weighted projective foliations
• Logarithmic Bundles Of Hypersurface Arrangements In P^n

Cited by in corpus (5)

• Polynomial bounds for automorphisms groups of foliations
• Global residue formula for logarithmic indices of foliations
• Computing Regular Meromorphic Differential Forms via Saito's Logarithmic Residues
• On Gauss-Bonnet and Poincaré-Hopf type theorems for complex $\partial$-manifolds
• Analytic varieties invariant by foliations and Pfaff systems