Bounds and formulas for residues of singular holomorphic foliations and applications
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.