On the Poincare Problem for Foliations of General Type
classification
🧮 math.DS
math.AG
keywords
boundsdegreefirstgeneralintegraltypeadmitsalgebraic
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Let F be a holomorphic foliation of general type on CP(2) which admits a rational first integral. We provide bounds for the degree of the first integral of F just in function of the degree, the birational invariants of F and the geometric genus of a generic leaf. Similar bounds for invariant algebraic curves are also obtained and examples are given showing the necessity of the hypothesis.
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