Open Access
October 2007 Standard surfaces and nodal curves in symplectic 4-manifolds
M. Usher
J. Differential Geom. 77(2): 237-290 (October 2007). DOI: 10.4310/jdg/1191860395


Continuing the program of S. Donaldson and I. Smith, and M. Usher, we introduce refinements of the Donaldson-Smith standard surface count which are designed to count nodal pseudoholomorphic curves and curves with a prescribed decomposition into reducible components. In cases where a corresponding analogue of the Gromov-Taubes invariant is easy to define, our invariants agree with those analogues. We also prove a vanishing result for some of the invariants that count nodal curves.


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M. Usher. "Standard surfaces and nodal curves in symplectic 4-manifolds." J. Differential Geom. 77 (2) 237 - 290, October 2007.


Published: October 2007
First available in Project Euclid: 8 October 2007

zbMATH: 1151.53073
MathSciNet: MR2355785
Digital Object Identifier: 10.4310/jdg/1191860395

Rights: Copyright © 2007 Lehigh University

Vol.77 • No. 2 • October 2007
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