Pardini, Rita Some remarks on plane curves over fields of finite characteristic. (English) Zbl 0607.14023 Compos. Math. 60, 3-17 (1986). 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 Cited in 3 ReviewsCited in 19 Documents MSC: 14E05 Rational and birational maps 14G15 Finite ground fields in algebraic geometry Keywords:reflexive curve; Weierstrass point; dual curve; characteristic p PDF BibTeX XML Cite \textit{R. Pardini}, Compos. Math. 60, 3--17 (1986; Zbl 0607.14023) Full Text: Numdam EuDML References: [1] R. Hartshorne : Algebraic geometry . Graduate texts in mathematics. Springer Verlag, New York (1977). · Zbl 0367.14001 [2] D. Laksov : Weierstrass points on curves . Astérisque, Vol. 87-88: (1981) 249-355. · Zbl 0489.14007 [3] D. Laksov : Wronskians and Plucker formulas for linear systems on curves . Ann. Ec. Norm. Sup., 4 serie, t. 17: 45-66. · Zbl 0555.14008 · doi:10.24033/asens.1465 · numdam:ASENS_1984_4_17_1_45_0 · eudml:82136 [4] S. Kleiman : Algebraic geometry: Open problems . Proc. Ravello 1982. Springer L.N.M. 997 (1983). [5] A. Wallace : Tangency and duality over arbitrary fields . Proc. Lond. Math. Soc. (9) 6 (1956). · Zbl 0072.16002 · doi:10.1112/plms/s3-6.3.321 [6] R.J. Walker : Algebraic curves . Princeton University Press, Princeton (1956). · Zbl 0039.37701 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.