The Generic Rank of the Baum-Bott Map for Degree-2 Foliations on Even-Dimensional Projective Spaces

Midory Komatsudani-Quispe

Journal of Singularities
volume 20 (2020), 103-127

Received: 5 February 2019. Received in revised form: 23 February 2020.

DOI: 10.5427/jsing.2020.20f

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Abstract:

The Baum-Bott map associates to a one-dimensional foliation on a complex manifold its Baum-Bott indexes at each singular point. The generic rank of this map on the space of foliations on the projective plane is known. In this work, we give an upper bound of the generic rank of the map for higher-dimensional projective spaces. We also determine the generic rank for degree-2 foliations on higher even-dimensional projective spaces. Additionally, we study the rank at the Jouanolou foliation.

2010 Mathematical Subject Classification:

37F75

Key words and phrases:

Holomorphic foliations, Baum-Bott index, Baum-Bott map, generic rank, Jouanolou foliation

Author(s) information:

Midory Komatsudani-Quispe
Instituto Nacional de Matemática Pura e Aplicada
Estrada Dona Castorina 110, Jardim Botânico
Rio de Janeiro 22460-320, RJ - Brazil
email: midorykq@gmail.com