East Asian mathematical journal

  • 제40권3호
  • /
  • Pages.287-293
  • /
  • 2024
  • /
  • 1226-6973(pISSN)
  • /
  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

ON THE EQUATIONS DEFINING SOME RATIONAL CURVES OF MAXIMAL GENUS IN ℙ3

  • Wanseok LEE (Department of applied Mathematics, Pukyong National University, Daeyeon Campus) ;
  • Shuailing Yang (Department of applied Mathematics, Pukyong National University, Daeyeon Campus)
  • 투고 : 2024.01.16
  • 심사 : 2024.02.27
  • 발행 : 2024.05.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

For a nondegenerate irreducible projective variety, it is a classical problem to describe its defining equations and the syzygies among them. In this paper, we precisely determine a minimal generating set and the minimal free resolution of defining ideals of some rational curves of maximal genus in ℙ3.

키워드

과제정보

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.

참고문헌

  1. G. Castelnuovo, Ricerche di geometria sulle curve algebraiche, Atti R. Accad. Sci Torino 24 (1889), 196-223.
  2. D. Eisenbud and S. Goto, Linear free resolutions and minimal multiplicity. Journal of Algebra 88 (1984) 89-133.
  3. D. Eisenbud, M. Green, K. Hulek and S. Popescu, Restricting linear syzygies: algebra and geometry, Compositio Math. 141 (2005), 1460-1478.
  4. L. Ein and R. Lazarsfeld, Syzygies and Koszul cohomology of smooth projective varieties of arbitrary dimension. Invent. Math. 111 (1993), 51-67.
  5. R. Ferraro, Weil divisors on rational normal scrolls, Lecture Notes in Pure and Applied Mathematics, 217 (2001), 183-198.
  6. M. Green and R. Lazarsfeld, Some results on the syzygies of finite sets and algebraic curves. Compositio Math. 67 (1988), 301-314.
  7. M. Decker, G.M. Greuel and H. Schonemann, Singular 3-1-2 - A computer algebra system for polynomial computations. http://www.singular.uni-kl.de (2011).
  8. L.T. Hoa, On minimal free resolutions of projective varieties of degree = codimension+2. J. Pure Appl. Algebra 87 (1993), 241-250.
  9. W. Lee and S. Yang, Some rational curves of maximal genus in ℙ3. To appear in East Asian Math. J.
  10. D. Mumford, Lectures on curves on an algebraic surface. With a section by G. M. Bergman. Annals of Mathematics Studies, No. 59 Princeton University Press, Princeton, N.J. 1966 xi+200 pp.
  11. U. Nagel, Arithmetically Buchsbaum divisors on varieties of minimal degree, Trans. Am. Math. Soc. 351(1999), 4381-4409
  12. U. Nagel and Y. Pitteloud On graded Betti numbers and geometrical properties of projective varieties, Manuscripta Math.84(1994), no.3-4, 291-314.