Some remarks on plane curves over fields of finite characteristic. (English) Zbl 0607.14023

Let X be a curve over an algebraically closed field K and let \(X^*\) be its dual curve; that is the curve made up of associating to every smooth point its tangent line. Thus \(X^*\) becomes equipped with a map \(\phi: X\to X^*.\) If K has zero characteristic then it is a classical result that \(\phi\) is birational. If K has characteristic \(p>0\) then this result does not hold longer - those curves for which it does hold are called ”reflexive”. The paper under review is devoted to a general study of when a nonsingular curve is reflexive.
Reviewer: D.Goss


14E05 Rational and birational maps
14G15 Finite ground fields in algebraic geometry
Full Text: Numdam EuDML


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