Geometry & Topology 9 (2005) 483–491

DOI: 10.2140/gt.2005.9.483

Abstract

We study the growth of the genus zero Gromov–Witten invariants GW_nD of the projective plane P²_k blown up at k points (where D is a class in the second homology group of P²_k). We prove that, under some natural restrictions on D, the sequence log GW_nD is equivalent to λn log n, where λ=D•c₁(P²_k).

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

Publication

Received: 30 December 2004
Accepted: 25 March 2005
Published: 7 April 2005
Proposed: Yasha Eliashberg
Seconded: Leonid Polterovich, Simon Donaldson

Authors