Abstract.
Given a generic d-web Wd of degree n in ℂℙ2, we associate with it a triple (SWd, π|SWd, FWd), where SWd is a surface in ℙT*ℂℙ2, the projective cotangent bundle of ℂℙ2, π|SWd is the restriction of the natural projection ℙT*ℂℙ2 → ℂℙ2 to SWd and FWd is a foliation on SWd given by a special meromorphic 1-form. The main objective of this article is to calculate the total number of singularities and the sum of the indices of Baum–Bott for the foliation FWd in terms of d and n. These results are compared with the case d = 1 (foliation in ℂℙ2). We also calculate the total number of nodes and cusps of the projection π|SWd in terms of d and n.
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2000 Mathematics Subject Classification. Primary: 37F75, Secondary: 34M45.
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Yartey, J. Number of Singularities of a Generic Web on the Complex Projective Plane. J Dyn Control Syst 11, 281–296 (2005). https://doi.org/10.1007/s10883-005-4175-9
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DOI: https://doi.org/10.1007/s10883-005-4175-9