Let F be a holomorphic one-dimensional foliation on ℙn such that the components of its singular locus Σ are curves Ci and points pj . We determine the number of pj , counted with multiplicities, in terms of invariants of and C F i, assuming that F is special along the Ci. Allowing just one nonzero dimensional component on Σ, we also prove results on when the foliation happens to be determined by its singular locus.
Foliations by curves with curves as singularities
MAURICIO BARROS CORREA JUNIOR.
;
2014-01-01
Abstract
Let F be a holomorphic one-dimensional foliation on ℙn such that the components of its singular locus Σ are curves Ci and points pj . We determine the number of pj , counted with multiplicities, in terms of invariants of and C F i, assuming that F is special along the Ci. Allowing just one nonzero dimensional component on Σ, we also prove results on when the foliation happens to be determined by its singular locus.File in questo prodotto:
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