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Contact formulas for rational plane curves via stable maps

Susan Jane Colley·Lars Ernstrom·Gary Kennedy
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Abstract

We use stable maps, and their stable lifts to the Semple bundle variety of second-order curvilinear data, to calculate certain characteristic numbers for rational plane curves. These characteristic numbers involve first-order (tangency) and second-order (inflectional) conditions. Although they may be virtual, they may be used as inputs in an enumeratively significant formula for the number of rational curves having a triple contact with a specified plane curve and passing through 3d-3 general points.

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Susan Jane Colley, Lars Ernstrom, Gary Kennedy. 2000-04-28. Contact formulas for rational plane curves via stable maps. https://arxiv.org/abs/math/9909129

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