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Standard surfaces and nodal curves in symplectic 4-manifolds

Michael Usher
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Abstract

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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Michael Usher. 2004-07-28. Standard surfaces and nodal curves in symplectic 4-manifolds. https://arxiv.org/abs/math/0407494

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