DOI QR코드

DOI QR Code

CONICS ON A GENERAL HYPERSURFACE IN COMPLEX PROJECTIVE SPACES

  • Received : 2013.01.03
  • Published : 2013.11.30

Abstract

In this paper we consider the existence of smooth conics on a general hypersurface of degree d in $\mathbb{P}^n$.

Keywords

conic;general hypersurface;Hilbert scheme

References

  1. W. Barth and A. Vande Ven, Fano varieties of lines on hypersurfaces, Arch. Math. (Basel) 31 (1978/79), no. 1, 96-104.
  2. J. Harris, M. Roth, and J. Starr, Rational curves on hypersurfaces of low degree, J. Reine Angew. Math. 571 (2004), 73-106.
  3. R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, no. 52, Springer-Verlag, 1977.
  4. S. Katz, On the finiteness of rational curves on quintic threefolds, Compositio Math. 60 (1986), no. 2, 151-162.
  5. J. Kollar, Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 32, Springer-Verlag, 1996.

Acknowledgement

Supported by : Chungnam National University