| Abstrakt: |
We present enumerative results for holomorphic foliations by curves on ℙ n , n ≥ 3, with singularities of positive dimension. Some of the results presented improve previous ones due to Corrêa et al. (Annales de l'institut Fourier, 64(4):1781–1805, 2014) and Costa (Ann Fac Sci Toulouse, Math (6), 15(2):297–321, 2006). We also present an enumerative result bounding the number of isolated singularities in a projective subvariety invariant by a holomorphic foliation by curves on ℙ n with a singularity of positive dimension. Moreover, we construct a family of holomorphic foliations by curves on ℙ n with a singularity of a positive dimension where its Milnor number is exhibited. [ABSTRACT FROM AUTHOR] |
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