English

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

R2 v1 2026-06-22T17:07:12.339Z