A Caporaso–Harris type formula for relative refined invariants
[Une formule de type Caporaso–Harris pour les invariants raffinés relatifs]
Blomme, Thomas1
1 Université de Genève, Rue du Conseil Général 5-7, 1205 Genève (Suisse)
Annales de l'Institut Fourier, Online first, 27 p.

En 2015, G. Mikhalkin a introduit un compte raffiné des courbes rationnelles réelles dans les surfcaes toriques passant par certains points situés sur le bord de cette dernière. Le raffinement est apporté par la valeur d’un certain indice quantique. Le compte introduit s’avère ne pas dépendre de du choix des points, donnant lieu à un invariant. Il est alors possible de les calculer à la limite tropicale en utilisant le théorème de correspondance et la multiplicité de Block–Göttsche. Dans ce papier on donne une formule récursive qui permet de calculer ces invariants, ce qui donne un algorithme de calcul.

In 2015, G. Mikhalkin introduced a refined count for real rational curves in a toric surface which pass through some points on the toric boundary of the surface. The refinement is provided by the value of a so-called quantum index. Moreover, he proved that the result of this refined count does not depend on the choice of the points. The correspondence theorem allows one to compute these invariants using the tropical geometry approach and the refined Block–Göttsche multiplicities. In this paper we give a recursive formula for these invariants, that leads to an algorithm to compute them.

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Révisé le :
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DOI : 10.5802/aif.3693
Classification : 14M25, 14N10, 14T90, 14H99
Keywords: enumerative geometry, tropical refined invariants
Mots-clés : géométrie énumérative, invariants raffinés tropicaux, formule récursive

Blomme, Thomas 1

1 Université de Genève, Rue du Conseil Général 5-7, 1205 Genève (Suisse) 
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Blomme, Thomas. A Caporaso–Harris type formula for relative refined invariants. Annales de l'Institut Fourier, Online first, 27 p.

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