GSV-Index for Holomorphic Pfaff Systems

  • Maurício Corrêa

    Departamento de Matemática, Av. Antônio Carlos 6627, Universidade Federal de Minas Gerais, 30123-970 Belo Horizonte-MG, Brazil
  • Diogo da Silva Machado

    Departamento de Matemática, Universidade Federal de Viçosa, Avenida Peter Henry Rolfs, s/n-Campus Universitário, 36570-900 Viçosa-MG, Brazil
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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 Poincaré problem for Pfaff systems on projectives spaces.

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Maurício Corrêa, Diogo da Silva Machado, GSV-Index for Holomorphic Pfaff Systems. Doc. Math. 25 (2020), pp. 1011–1027

DOI 10.4171/DM/769