Local resolution at the quadrivalent vertices

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Table of contents

1 Introduction 
1.1 Historique
1.2 Cadre et Motivations
1.3 Résultats
1.4 Plan du manuscrit
2 Généralités et notations sur les variétés toriques 
2.1 Variétés toriques
2.2 Courbes paramétrées dans les variétés toriques
2.3 Structure réelle d’une variété torique
2.4 Amibes et Coamibes
3 Tropical geometry and tropical curves 
3.1 Tropical curves
3.2 The moduli of tropical curves and tropical enumerative geometry
3.3 Tropicalization
4 Computation of some refined invariants in toric surfaces 
4.1 Quantum indices of real rational curves
4.2 Refined curve counting in a toric surface
4.3 Realization and correspondence theorem in the real case
4.4 Statement of result and proof
5 Recursive formula for tropical refined invariants 
5.1 Definition of the invariants and recursive formula
5.2 Proof of the recursive formula
5.3 Computations
5.4 Recursive formulas for algebraic invariants
6 Curves in higher dimension 
6.1 Quantum class of type I real curve
6.2 Harnack curves in higher dimension
6.3 Enumerative problem
Bibliographie