Geodesic
The Generic Rank of the Baum-Bott Map for Degree-2 Foliations on Even-Dimensional Projective Spaces
Journal of Singularities, Tome 20 (2020), pp. 103-127

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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.
DOI : 10.5427/jsing.2020.20f
Classification : 37F75 
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     author = {Midory Komatsudani-Quispe},
     title = {The {Generic} {Rank} of the {Baum-Bott} {Map} for {Degree-2} {Foliations} on {Even-Dimensional} {Projective} {Spaces}},
     journal = {Journal of Singularities},
     pages = {103--127},
     publisher = {mathdoc},
     volume = {20},
     year = {2020},
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Midory Komatsudani-Quispe. The Generic Rank of the Baum-Bott Map for Degree-2 Foliations on Even-Dimensional Projective Spaces. Journal of Singularities, Tome 20 (2020), pp. 103-127. doi: 10.5427/jsing.2020.20f

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