On diagonal cubic surfaces

Research output: Contribution to journalArticle

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Abstract

We show that the affine surfaces x3+y3+cz3=c, c ∈Q, in the cases c≠2, c=2, contain precisely 2, respectively 4, polynomial parametric solutions corresponding to curves of arithmetic genus 0 on the surface. However, these surfaces contain infinitely many polynomial parametric solutions corresponding to curves of arithmetic genus greater than 0.

Original languageEnglish (US)
Pages (from-to)21-32
Number of pages12
JournalManuscripta Mathematica
Volume62
Issue number1
DOIs
StatePublished - Mar 1 1988

ASJC Scopus subject areas

  • Mathematics(all)

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