The number of plane conics 5-fold tangent to a given curve

Details The number of plane conics 5-fold tangent to a given curve The number of plane conics 5-fold tangent to a given curve

2002-01-31

arxiv.org/abs/math/0202002v1

Mathematics

Algebraic Geometry

16 pages

Scientific paper

Given a general plane curve Y of degree d, we compute the number n_d of irreducible plane conics that are 5-fold tangent to Y. This problem has been studied before by Vainsencher using classical methods, but it could not be solved there because the calculations received too many non-enumerative correction terms that could not be analyzed. In our current approach, we express the number n_d 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 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 P^2, and compare this number to the corresponding Yau-Zaslow K3 invariant. This gives an example of such a K3 invariant for a non-primitive homology class.

Affiliated with

Also associated with

No associations

Rating

The number of plane conics 5-fold tangent to a given curve does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The number of plane conics 5-fold tangent to a given curve, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The number of plane conics 5-fold tangent to a given curve will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-423731