AN OBSTRUCTION BUNDLE RELATING GROMOV-WITTEN INVARIANTS OF CURVES AND KÄHLER SURFACES

In a previous paper the authors defined symplectic "Local Gromov-Witten invariants" associated to spin curves and showed that the GW invariants of a Kahler surface X with p g > 0 are a sum of such local GW invariants. This paper describes how the local GW invariants arise from an obstru...

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Bibliographic Details
Published in:American journal of mathematics Vol. 134; no. 2; pp. 453 - 506
Main Authors: Lee, Junho, Parker, Thomas H.
Format: Journal Article
Language:English
Published: Baltimore Johns Hopkins University Press 01.04.2012
Subjects:
Algebra
Coordinate systems
Cylinders
Geometry
Linear algebra
Linearization
Mathematical manifolds
Mathematical vectors
Mathematics
Numerical analysis
Perceptron convergence procedure
Topological compactness
Vector spaces
ISSN:0002-9327, 1080-6377, 1080-6377
Online Access:Get full text
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Summary:In a previous paper the authors defined symplectic "Local Gromov-Witten invariants" associated to spin curves and showed that the GW invariants of a Kahler surface X with p g > 0 are a sum of such local GW invariants. This paper describes how the local GW invariants arise from an obstruction bundle (in the sense of Taubes) over the space of stable maps into curves. Together with the results of our earlier paper, this reduces the calculation of the GW invariants of elliptic and generaltype complex surfaces to computations in the GW theory of curves with additional classes: the Euler classes of the (real) obstruction bundles.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.2012.0010