Foliations with isolated singularities on Hirzebruch surfaces
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Foliations with isolated singularities on Hirzebruch surfacesFecha de publicación
2021Editor
De GruyterCita bibliográfica
Galindo, Carlos, Monserrat, Francisco and Olivares, Jorge. "Foliations with isolated singularities on Hirzebruch surfaces" Forum Mathematicum, vol. 33, no. 6, 2021, pp. 1471-1486. https://doi.org/10.1515/forum-2021-0135Tipo de documento
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Resumen
We study foliations ℱ on Hirzebruch surfaces Sδ and prove that, similarly to those on the projective plane, any ℱ can be represented by a bi-homogeneous polynomial affine 1-form. In case ℱ has isolated singularities, ... [+]
We study foliations ℱ on Hirzebruch surfaces Sδ and prove that, similarly to those on the projective plane, any ℱ can be represented by a bi-homogeneous polynomial affine 1-form. In case ℱ has isolated singularities, we show that, for δ=1, the singular scheme of ℱ does determine the foliation, with some exceptions that we describe, as is the case of foliations in the projective plane. For δ≠1, we prove that the singular scheme of ℱ does not determine the foliation. However, we prove that, in most cases, two foliations ℱ and ℱ′ given by sections s and s′ have the same singular scheme if and only if s′=Φ(s), for some global endomorphism Φ of the tangent bundle of Sδ. [-]
Publicado en
Forum Math. 2021; 33(6)Entidad financiadora
Ministerio de Ciencia, Innovación y Universidades (Spain) | Generalitat Valenciana | Universitat Jaume I | Consejo Nacional de Ciencia y Tecnología
Código del proyecto o subvención
PGC2018-096446-B-C22 | RED2018-102583-T | AICO-2019-223 | UJI-2018-10 | CVU 10069
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
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