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1999•Canadian Journal of MathematicsOpen access

The Characteristic Numbers of Quartic Plane Curves

Ravi Vakil

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Abstract

Abstract The characteristic numbers of smooth plane quartics are computed using intersection theory on a component of the moduli space of stable maps. This completes the verification of Zeuthen’s prediction of characteristic numbers of smooth plane curves. A short sketch of a computation of the characteristic numbers of plane cubics is also given as an illustration.

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Abstract The characteristic numbers of smooth plane quartics are computed using intersection theory on a component of the moduli space of stable maps. This completes the verification of Zeuthen’s prediction of characteristic numbers of smooth plane curves. A short sketch of a computation of the characteristic numbers of plane cubics is also given as an illustration.

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Available abstract

Abstract The characteristic numbers of smooth plane quartics are computed using intersection theory on a component of the moduli space of stable maps. This completes the verification of Zeuthen’s prediction of characteristic numbers of smooth plane curves. A short sketch of a computation of the characteristic numbers of plane cubics is also given as an illustration.

Key concepts: Quartic function, Mathematics, Plane curve, Moduli space, Intersection (aeronautics), Plane (geometry), Quartic plane curve, Computation

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