Foliations with isolated singularities on Hirzebruch surfaces
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Show full item recordcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
Foliations with isolated singularities on Hirzebruch surfacesDate
2021Publisher
De GruyterBibliographic citation
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-2021-0135Type
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info:eu-repo/semantics/publishedVersionSubject
Abstract
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. [-]
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Forum Math. 2021; 33(6)Funder Name
Ministerio de Ciencia, Innovación y Universidades (Spain) | Generalitat Valenciana | Universitat Jaume I | Consejo Nacional de Ciencia y Tecnología
Project code
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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