Standard surfaces and nodal curves in symplectic 4-manifolds

Details Standard surfaces and nodal curves in symplectic 4-manifolds Standard surfaces and nodal curves in symplectic 4-manifolds

2004-07-28

arxiv.org/abs/math/0407494v3

J. Differential Geom. 77 (2007), no. 2, 237--290

Mathematics

Symplectic Geometry

Technical details needed for the proofs of some results in Section 3 have been added in Section 6. 43 pages

Scientific paper

Continuing the program of math.SG/0012067 and math.SG/0310450, 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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