Sheaves associated to holomorphic first integrals
Copyright policy )Sheaves associated to holomorphic first integrals
Let ℱ : L → T S be a foliation on a complex, smooth and irreducible projective surface S , assume ℱ admits a holomorphic first integral f : S → ℙ 1 . If h 0 ( S , 𝒪 S ( - n 𝒦 S ) ) > 0 for some n ≥ 1 we prove the inequality: ( 2 n - 1 ) ( g - 1 ) ≤ h 1 ( S , ℒ ′ - 1 ( - ( n - 1 ) K S ) ) + h 0 ( S , ℒ ′ ) + 1 . If S is rational we prove that the direct image sheaves of the co-normal sheaf of ℱ under f are locally free; and give some information on the nature of their decomposition as direct sum of invertible sheaves.
Geometric methods in ordinary differential equations, holomorphic foliations, first integrals, Dynamical aspects of holomorphic foliations and vector fields, Curves in algebraic geometry
Geometric methods in ordinary differential equations, holomorphic foliations, first integrals, Dynamical aspects of holomorphic foliations and vector fields, Curves in algebraic geometry
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