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

    Cadman, Charles and Chen, Linda 2008. Enumeration of rational plane curves tangent to a smooth cubic. Advances in Mathematics, Vol. 219, Issue. 1, p. 316.


    Ayala, David and Cavalieri, Renzo 2006. Counting bitangents with stable maps. Expositiones Mathematicae, Vol. 24, Issue. 4, p. 307.


    Lee, Junho and Leung, Naichung Conan 2005. Yau–Zaslow formula on K3 surfaces for non-primitive classes. Geometry & Topology, Vol. 9, Issue. 4, p. 1977.


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The number of plane conics that are five-fold tangent to a given curve

  • Andreas Gathmann (a1)
  • DOI: http://dx.doi.org/10.1112/S0010437X04001083
  • Published online: 01 February 2005
Abstract

Given a general plane curve Y of degree d, we compute the number nd of irreducible plane conics that are five-fold tangent to Y. This problem has been studied before by Vainsencher using classical methods, but it could not be solved because the calculations produced too many non-enumerative correction terms that could not be analyzed. In our current approach, we express the number nd in terms of relative Gromov–Witten invariants that can then be directly computed. As an application, we consider the K3 surface given as the double cover of $\mathbb{P}^2$ branched along a sextic curve. We compute the number of rational curves in this K3 surface in the homology class that is the pull-back of conics in $\mathbb{P}^2$, and compare this number with the corresponding Yau–Zaslow K3 invariant. This gives an example of such a K3 invariant for a non-primitive homology class.

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