An Analogous of Jouanolou’s Theorem in Positive Characteristic
نویسنده
چکیده
We show that a generic vector field on an affine space of positive characteristic admits an invariant algebraic hypersurface. This contrast with Jouanolou’s Theorem that shows that in characteristic zero the situation is completely opposite. That is a generic vector field in the complex plane does not admit any invariant algebraic curve.
منابع مشابه
Invariant Hypersurfaces for Positive Characteristic Vector Fields
We show that a generic vector field on an affine space of positive characteristic admits an invariant algebraic hypersurface. This is in sharp contrast with the characteristic zero case where Jouanolou’s Theorem says that a generic vector field on the complex plane does not admit any invariant algebraic curve.
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تاریخ انتشار 2000