Geodesic
GSV-Index for Holomorphic Pfaff Systems
Documenta mathematica, Tome 25 (2020), pp. 1011-1027.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 58A17, 32S65, 32M25, 37F75, 37B30
Keywords: Pfaff systems, foliations, residues, invariant varieties 
@article{DOCMA_2020__25__a38,
     author = {Corr\^ea, Maur{\'\i}cio and da Silva Machado, Diogo},
     title = {GSV-Index for {Holomorphic} {Pfaff} {Systems}},
     journal = {Documenta mathematica},
     pages = {1011--1027},
     publisher = {mathdoc},
     volume = {25},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a38/}
}
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Corrêa, Maurício; da Silva Machado, Diogo. GSV-Index for Holomorphic Pfaff Systems. Documenta mathematica, Tome 25 (2020), pp. 1011-1027. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a38/