East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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SOME RATIONAL CURVES OF MAXIMAL GENUS IN ℙ3

  • Wanseok LEE (Department of applied Mathematics, Pukyong National University) ;
  • Shuailing Yang (Department of applied Mathematics, Pukyong National University)
  • Received : 2023.10.10
  • Accepted : 2023.11.10
  • Published : 2024.01.31
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Abstract

For a reduced, irreducible and nondegenerate curve C ⊂ ℙr of degree d, it was shown that the arithmetic genus g of C has an upper bound π0(d, r) by G. Castelnuovo. And he also classified the curves that attain the extremal value. These curves are arithmetically Cohen-Macaulay and contained in a surface of minimal degree. In this paper, we investigate the arithmetic genus of curves lie on a surface of minimal degree - the Veronese surface, smooth rational normal surface scrolls and singular rational normal surface scrolls. We also provide a construction of curves on singular rational normal surface scroll S(0, 2) ⊂ ℙ3 which attain the maximal arithmetic genus.

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Acknowledgement

This work was supported by Pukyong National University Research Fund in 2020. The authors are grateful to the referees for their careful reading of the manuscript and the suggesting improvements.

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