Comptes Rendus
no. 6
Algebraic Geometry
Enumeration of curves via floor diagrams
[Énumération de courbes par des diagrammes en étages]

Présenté par : Maxime Kontsevitch

Erwan Brugallé1 ; Grigory Mikhalkin2
1 Université Pierre-et-Marie-Curie, Institut mathématiques de Jussieu, 175, rue du Chevaleret, 75013 Paris, France
2 University of Toronto, Department of Mathematics, 40 St. George St., Toronto, Ontario M5S 2E4, Canada
Comptes Rendus. Mathématique, Volume 345 (2007) no. 6, pp. 329-334.

Dans cette Note nous calculons certains invariants énumératifs d'espaces projectifs réels et complexes en termes de graphes enrichis appelés diagrammes en étages.

In this Note we compute some enumerative invariants of real and complex projective spaces by means of some enriched graphs called floor diagrams.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.07.026
Erwan Brugallé 1 ; Grigory Mikhalkin 2

1 Université Pierre-et-Marie-Curie, Institut mathématiques de Jussieu, 175, rue du Chevaleret, 75013 Paris, France
2 University of Toronto, Department of Mathematics, 40 St. George St., Toronto, Ontario M5S 2E4, Canada 
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Erwan Brugallé; Grigory Mikhalkin. Enumeration of curves via floor diagrams. Comptes Rendus. Mathématique, Volume 345 (2007) no. 6, pp. 329-334. doi : 10.1016/j.crma.2007.07.026. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.07.026/

[1] E. Brugallé, G. Mikhalkin, Floor decomposition of tropical curves, in preparation

[2] L. Caporaso; J. Harris Counting plane curves of any genus, Invent. Math., Volume 131 (1998), pp. 345-392

[3] I. Itenberg; V. Kharlamov; E. Shustin Welschinger invariant and enumeration of real rational curves, Int. Math. Res. Not., Volume 49 (2003), pp. 2639-2653

[4] M. Kontsevich; Yu. Manin Gromov–Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys., Volume 164 (1994), pp. 525-562

[5] G. Mikhalkin Enumerative tropical algebraic geometry in R2, J. Amer. Math. Soc., Volume 18 (2005), pp. 313-377

[6] I. Vainsencher Enumeration of n-fold tangent hyperplanes to a surface, J. Algebraic Geom., Volume 4 (1995), pp. 503-526

[7] J.Y. Welschinger Invariants of real symplectic 4-manifolds and lower bounds in real enumerative geometry, Invent. Math., Volume 162 (2005), pp. 195-234

[8] J.Y. Welschinger Spinor states of real rational curves in real algebraic convex 3-manifolds and enumerative invariants, Duke Math. J., Volume 127 (2005), pp. 89-121

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