Volume 9, issue 1 (2005)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Logarithmic asymptotics of the genus zero Gromov–Witten invariants of the blown up plane

Ilia Itenberg, Viatcheslav Kharlamov and Eugenii Shustin

Geometry & Topology 9 (2005) 483–491

arXiv: math.AG/0412533

Abstract

We study the growth of the genus zero Gromov–Witten invariants GWnD of the projective plane Pk2 blown up at k points (where D is a class in the second homology group of Pk2). We prove that, under some natural restrictions on D, the sequence logGWnD is equivalent to λnlogn, where λ = D c1(Pk2).

Keywords
Gromov–Witten invariants, rational, ruled algebraic surfaces, rational, ruled symplectic 4–manifolds, tropical enumerative geometry
Mathematical Subject Classification 2000
Primary: 14N35
Secondary: 14J26, 53D45
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Publication
Received: 30 December 2004
Accepted: 25 March 2005
Published: 7 April 2005
Proposed: Yasha Eliashberg
Seconded: Leonid Polterovich, Simon Donaldson
Authors
Ilia Itenberg
Université Louis Pasteur et IRMA
7, rue René Descartes
67084 Strasbourg Cedex
France
Viatcheslav Kharlamov
Université Louis Pasteur et IRMA
7, rue René Descartes
67084 Strasbourg Cedex
France
Eugenii Shustin
School of Mathematical Sciences
Tel Aviv University
Ramat Aviv
69978 Tel Aviv
Israel