Foliations with isolated singularities on Hirzebruch surfaces

[EN] We study foliations F on Hirzebruch surfaces Sd 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 delta = 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 delta not equal 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' = Phi(s), for some global endomorphism F of the tangent bundle of S-delta.The first two authors are partially supported by the Spanish Government MICINN/FEDER/AEI/UE, grants PGC2018-096446-B-C22 and RED2018-102583-T, as well as by Generalitat Valenciana, grant AICO2019-223 and Universitat Jaume I, grantUJI-2018-10. The third authorwas partially supported by CONACYT: Estancias Sabaticas Vinculadas a la Consolidacion de Grupos de Investigacion, CVU 10069.Galindo Pastor, C.; Monserrat Delpalillo, FJ.; Olivares, J. (2021). Foliations with isolated singularities on Hirzebruch surfaces. Forum Mathematicum. 33(6):1471-1486. https://doi.org/10.1515/forum-2021-01351471148633