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  • Cited by 2
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Tyomkin, I. 2010. On Severi Varieties on Hirzebruch Surfaces. International Mathematics Research Notices,

    Ran, Z. 2001. On the variety of rational space curves. Israel Journal of Mathematics, Vol. 122, Issue. 1, p. 359.


Parameter spaces for curves on surfaces and enumeration of rational curves

  • DOI:
  • Published online: 01 September 1998

Let S be a smooth, minimal rational surface. The geometry of the Severi variety parametrising irreducible, rational curves in a given linear system on S is studied. The results obtained are applied to enumerative geometry, in combination with ideas from Quantum Cohomology. Formulas enumerating rational curves are found, some of which generalised Kontsevich‘s formula for plane curves.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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