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Pàgina inicial > Articles > Articles publicats > Convex foliations of degree 5 on the complex projective plane |
Data: | 2021 |
Resum: | We show that, up to automorphisms of P2 C, there are fourteen homogeneous convex foliations of degree 5 on P2 C. We establish some properties of the Fermat foliation Fd 0 of degree d ≥ 2 and of the Hilbert modular foliation F5 H of degree 5. As a consequence, we obtain that every reduced convex foliation of degree 5 on P2 C is linearly conjugated to one of the two foliations F5 0 or F5 H, which is a partial answer to a question posed in 2013 by D. Marín and J. V. Pereira. We end with two conjectures about the Camacho-Sad indices along the line at infinity at the non radial singularities of the homogeneous convex foliations of degree d ≥ 2 on P2C. |
Ajuts: | Ministerio de Ciencia e Innovación MTM2015-66165-P Ministerio de Ciencia e Innovación PGC2018-095998-B-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1725 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió publicada |
Publicat a: | Publicacions matemàtiques, Vol. 65 Núm. 2 (2021) , p. 409-429 (Articles) , ISSN 2014-4350 |
21 p, 448.5 KB |