Bounds and formulas for residues of singular holomorphic foliations and applications

2025/03/09 by Machado, Diogo da Silva · 1 citation
#37F75 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 32S65 #secundary 14F05

paper · doi:10.48550/arxiv.2503.06585

Abstract

We consider one dimensional holomorphic foliations with isolated singularities that leave invariant a local complete intersection. We establish explicit formulas for the total GSV index of such foliations and obtain bounds for this index. As applications, we derive several consequences related to Poincaré's problem for foliations on projective spaces.

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• On some indices of foliations and applications

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