Abstract
We prove that a foliation 877-1 of degree ≠ 1 on P 2 is completely determined by its singular subscheme SingS( 877-2) of P 2. We apply this result to obtain a similar characterization of 877-3 in terms of the configuration of base points associated to its singular scheme, in case every singularity of 877-4 has non-trivial linear part. Our main motivation comes from a well-known fact: in case a foliation 877-5 of degree r ≥ 2 on P n has only isolated singularities of multiplicity 1, then 877-6 is completely determined by its singular set Sing( 877-7).
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