Volume 9 (2005)
Download this article
For screen
For printing
Recent Issues

Volume 16 (2012)
Issue 1 1–

Volume 15 (2011) 1–4

Volume 14 (2010) 1–5

Volume 13 (2009) 1–5

Volume 12 (2008) 1–5

Volume 11 (2007)

Volume 10 (2006)

Volume 9 (2005)

Volume 8 (2004)

Volume 7 (2003)

Volume 6 (2002)

Volume 5 (2001)

Volume 4 (2000)

Volume 3 (1999)

Volume 2 (1998)

Volume 1 (1997)

G&T Monographs
The Journal
About the Journal
Editorial Board
Editorial Interests
Author Index
Editorial procedure
Submission Guidelines
Submission Page
Author copyright form
Subscriptions
Contacts
G&T Publications
GTP Author Index

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

DOI: 10.2140/gt.2005.9.483

arXiv: math.AG/0412533
Abstract

We study the growth of the genus zero Gromov–Witten invariants GWnD of the projective plane P2k blown up at k points (where D is a class in the second homology group of P2k). We prove that, under some natural restrictions on D, the sequence log GWnD is equivalent to λn log n, where λ=D•c1(P2k).

Keywords

Gromov–Witten invariants, rational, ruled algebraic surfaces, rational, ruled symplectic 4–manifolds, tropical enumerative geometry
Mathematical Subject Classification

Primary: 14N35

Secondary: 14J26, 53D45
References
Forward citations
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