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Some characteristic numbers for nodal and cuspidal plane curves of any degree

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Abstract

Two blow-ups over the projective spaceP N parametrizing plane curves of a given degree yield a compactification of the space of reduced curves used in [2] to obtain partial enumerative results for families of non-singular plane curves. In this paper it is shown how to employ the construction to obtain enumerative results for families of plane curves with a node or a cusp. The results recover known results for cubics, give a first modern verification of some computations of of Zeuthen’s for quartics, and are new for higher degree. The heart of the computation is the derivation of key Segre classes relating the intersection calculus at the different stages of the blow-up construction.

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References

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Authors and Affiliations

  1. Mathematics Department, Oklahoma State University, 74078, Stillwater, OK

    Paolo Aluffi

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  1. Paolo Aluffi
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The author was partially supported by the DFG Forschungsschwerpunkt Komplexe Mannig-faltigkeiten during the preparation of this manuscript

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Aluffi, P. Some characteristic numbers for nodal and cuspidal plane curves of any degree. Manuscripta Math 72, 425–444 (1991). https://doi.org/10.1007/BF02568288

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  • DOI: https://doi.org/10.1007/BF02568288

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