Proximity inequalities and bounds for the degree of invariant curves by foliations of ℙ_ {ℂ} ²
A Campillo, M Carnicer - Transactions of the American Mathematical …, 1997 - ams.org
Transactions of the American Mathematical Society, 1997•ams.org
In this paper we prove that if $ C $ is a reduced curve which is invariant by a foliation
$\mathcal F $ in the complex projective plane then one has $\partial^{\underline {\circ}}
C\leq\partial^{\underline {\circ}}\mathcal F+ 2+ a $ where $ a $ is an integer obtained from a
concrete problem of imposing singularities to projective plane curves. If $\mathcal F $ is
nondicritical or if $ C $ has only nodes as singularities, then one gets $ a= 0$ and we
recover known bounds. We also prove proximity formulae for foliations and we use these …
$\mathcal F $ in the complex projective plane then one has $\partial^{\underline {\circ}}
C\leq\partial^{\underline {\circ}}\mathcal F+ 2+ a $ where $ a $ is an integer obtained from a
concrete problem of imposing singularities to projective plane curves. If $\mathcal F $ is
nondicritical or if $ C $ has only nodes as singularities, then one gets $ a= 0$ and we
recover known bounds. We also prove proximity formulae for foliations and we use these …
Abstract
In this paper we prove that if is a reduced curve which is invariant by a foliation in the complex projective plane then one has where is an integer obtained from a concrete problem of imposing singularities to projective plane curves. If is nondicritical or if has only nodes as singularities, then one gets and we recover known bounds. We also prove proximity formulae for foliations and we use these formulae to give relations between local invariants of the curve and the foliation. References
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