Logarithmic asymptotics of the genus zero Gromov–Witten invariants of the blown up plane

Itenberg, Ilia¹ ; Kharlamov, Viatcheslav¹ ; Shustin, Eugenii²

¹ Université Louis Pasteur et IRMA, 7, rue René Descartes, 67084 Strasbourg Cedex, France
² School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel

Geometry & topology, Tome 9 (2005) no. 1, pp. 483-491.

Résumé

We study the growth of the genus zero Gromov–Witten invariants $G{W}_{nD}$ of the projective plane $P_k^2$ blown up at $k$ points (where $D$ is a class in the second homology group of $P_k^2$). We prove that, under some natural restrictions on $D$, the sequence $logG{W}_{nD}$ is equivalent to $\lambda nlogn$, where $\lambda =D\cdot c_1\left(P_k^2\right)$.

Détail

DOI : 10.2140/gt.2005.9.483

Keywords: Gromov–Witten invariants, rational, ruled algebraic surfaces, rational, ruled symplectic 4–manifolds, tropical enumerative geometry

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