Counting rational curves with an m-fold point

Counting rational curves with an m-fold point

We obtain a recursive formula for the number of rational curves of degree d in CP2, that pass through 3d+1−m generic points and that have an m-fold singular point. The special case of counting curves with a triple point was solved earlier by other authors. We obtain the formula by considering a fami...

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2023-10, Vol.431, p.109258, Article 109258
Hauptverfasser: Biswas, Indranil, Chaudhuri, Chitrabhanu, Choudhury, Apratim, Mukherjee, Ritwik, Paul, Anantadulal
Format: Artikel
Sprache:eng
Schlagworte:
Enumerative geometry
Gromov-Witten invariants
Singularity
WDVV equation
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Zusammenfassung:We obtain a recursive formula for the number of rational curves of degree d in CP2, that pass through 3d+1−m generic points and that have an m-fold singular point. The special case of counting curves with a triple point was solved earlier by other authors. We obtain the formula by considering a family version of Kontsevich's recursion formula, in contrast to the excess intersection theoretic approach of others. A large number of low degree cases have been worked out explicitly.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2023.109258