GSV-index for holomorphic Pfaff Systems
Algebraic Geometry
2020-10-06 v4 Complex Variables
Dynamical Systems
Abstract
In this work we introduce a GSV type index for varieties invariant by holomorphic Pfaff systems (possibly non locally decomposables) on projective manifolds. We prove a non-negativity property for the index. As an application, we prove that the non-negativity of the GSV-index gives us an obstruction to the solution of the Poincar\'e problem for Pfaff systems on projectives spaces.
Cite
@article{arxiv.1611.09376,
title = {GSV-index for holomorphic Pfaff Systems},
author = {Maurício Corrêa and Diogo da Silva Machado},
journal= {arXiv preprint arXiv:1611.09376},
year = {2020}
}
Comments
15 pages; to appear in Documenta Mathematica. Major changes following suggestions of the referees