The Journal of the Indian Mathematical Society

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On Linear Complexes of Minimum Rank Containing all the Tangents of a Rational Norm Curve


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1 Annamalai University, India
     

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The rational curve Rn(3) of order n in [3], whose tangents belong to a linear complex, has been studied in detail by several writers. Picard showed that such a curve possesses in general 2n-6 points of inflexion. G. H. Grace attempted to prove the converse, that if an Rn(3) has 2n-6 inflexions its tangents belong to a linear complex. The proof was however faulty, and M. F. Egan gave an example of a sextic curve for which the converse theorem is not true.
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  • On Linear Complexes of Minimum Rank Containing all the Tangents of a Rational Norm Curve

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Authors

B. Ramamurthi
Annamalai University, India

Abstract


The rational curve Rn(3) of order n in [3], whose tangents belong to a linear complex, has been studied in detail by several writers. Picard showed that such a curve possesses in general 2n-6 points of inflexion. G. H. Grace attempted to prove the converse, that if an Rn(3) has 2n-6 inflexions its tangents belong to a linear complex. The proof was however faulty, and M. F. Egan gave an example of a sextic curve for which the converse theorem is not true.