GSV-Index for Holomorphic Pfaff Systems

GSV-Index for Holomorphic Pfaff Systems

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...

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Veröffentlicht in:Documenta mathematica Journal der Deutschen Mathematiker-Vereinigung. 2020, Vol.25, p.1011-1027
Hauptverfasser: Corrêa, Maurício, da Silva Machado, Diogo
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1431-0635
1431-0643
DOI:10.4171/dm/769