Geodesic
GSV-Index for Holomorphic Pfaff Systems
Documenta mathematica, Tome 25 (2020), pp. 1011-1027
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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.
DOI : 10.4171/dm/769
Classification : 32M25, 32S65, 37B30, 37F75, 58A17
Mots-clés : residues, Pfaff systems, foliations, invariant varieties 
@article{10_4171_dm_769,
     author = {Diogo da Silva Machado and Maur{\'\i}cio Corr\^ea},
     title = {GSV-Index for {Holomorphic} {Pfaff} {Systems}},
     journal = {Documenta mathematica},
     pages = {1011--1027},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/769},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/769/}
}
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Diogo da Silva Machado; Maurício Corrêa. GSV-Index for Holomorphic Pfaff Systems. Documenta mathematica, Tome 25 (2020), pp. 1011-1027. doi: 10.4171/dm/769

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