The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

FACTORIAL NODAL COMPLETE INTERSECTION 3-FOLDS IN ℙ5

  • Hong, Kyusik (Department of Mathematics Education, Jeonju University)
  • Received : 2022.04.12
  • Accepted : 2022.04.26
  • Published : 2022.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

Let X be a nodal complete intersection 3-fold defined by a hypersurface in ℙ5 of degree n and a smooth quadratic hypersurface in ℙ5 . Then we show that X is factorial if it has at most n2 - n + 1 nodes and contains no 2-planes, where n = 3, 4.

Keywords

References

  1. Cheltsov, I.: Factoriality of nodal three-dimensional varieties and connectedness of the locus of log canonical singularities. Mat. Sb. 197 (2006), 387-414. https://doi.org/10.1070/SM2006v197n03ABEH003763
  2. Cheltsov, I.: Factorial threefold hypersurfaces. J. Algebraic Geom. 19 (2010), 781-791. https://doi.org/10.1090/S1056-3911-09-00522-0
  3. Cheltsov, I.: On a conjecture of Ciliberto. Sb. Math. 201 (2010), 1069-1090. https://doi.org/10.1070/SM2010v201n07ABEH004103
  4. Cynk, S.: Defect of a nodal hypersurface. Manuscripta Math. 104 (2001), 325-331. https://doi.org/10.1007/s002290170030
  5. Cynk, S. & Rams, S.: Non-factorial nodal complete intersection threefolds. Commun. Contemp. Math. 15, no. 5, 1250064, 14 pp (2013) https://doi.org/10.1142/S0219199712500642
  6. Edmonds, J.: Minimum partition of a matroid into independent subsets. J. Res. Nat. Bur. Standards Sect. B 69 B (1965), 67-72. https://doi.org/10.6028/jres.069B.004
  7. Eisenbud, D. & Koh, J.-H.: Remarks on points in a projective space. in: Communicative Algebra, Berkeley, CA, in: Mathematical Science Research Institute Publications, vol. 15, Springer, New York, 1987, pp. 157-172.
  8. Kloosterman, R.: Nodal complete intersection threefold with defect. arXiv preprint arXiv:1503.05420. (2015), 1-21.
  9. Kosta, D.: Factoriality of complete intersections in ℙ5. Proc. Steklov Inst. Math. 264 (2009), 102-109. https://doi.org/10.1134/S0081543809010131