On the characterization of algebraically integrable plane foliations
نویسندگان
چکیده
منابع مشابه
On the Characterization of Algebraically Integrable Plane Foliations
We give a characterization theorem for non-degenerate plane foliations of degree different from 1 having a rational first integral. Moreover, we prove that the degree r of a non-degenerate foliation as above provides the minimum number, r+ 1, of points in the projective plane through which pass infinitely many algebraic leaves of the foliation.
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We give an algorithm to decide whether an algebraic plane foliation F has a rational first integral and to compute it in the affirmative case. The algorithm runs whenever we assume the polyhedrality of the cone of curves of the surface obtained after blowing-up the set BF of infinitely near points needed to get the dicritical exceptional divisors of a minimal resolution of the singularities of ...
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This paper contributes to the solution of the Poincaré problem, which is to bound the degree of a (generalized algebraic) leaf of a (singular algebraic) foliation of the complex projective plane. The first theorem gives a new sort of bound, which involves the Castelnuovo–Mumford regularity of the singular locus of the leaf. The second theorem gives a bound in terms of two singularity numbers of...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2010
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-10-04808-7