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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Vydáno v:American journal of mathematics Ročník 134; číslo 2; s. 453 - 506
Hlavní autoři: Lee, Junho, Parker, Thomas H.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Baltimore Johns Hopkins University Press 01.04.2012
Témata:
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
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Abstract 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.
AbstractList In a previous paper the authors defined symplectic ``Local Gromov-Witten invariants'' associated to spin curves and showed that the GW invariants of a K\"ahler 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 general-type complex surfaces to computations in the GW theory of curves with additional classes: the Euler classes of the (real) obstruction bundles.
In a previous paper the authors defined symplectic "Local Gromov-Witten invariants" associated to spin curves and showed that the GW invariants of a Kähler surface X with p^sub g^ > 0 are asum of such local GW invariants. This paper describes how the local GW invariants arise from an obstructionbundle (in the sense of Taubes) over the space of stable maps into curves. Together with theresults of our earlier paper, this reduces the calculation of the GW invariants of elliptic and general-typecomplex surfaces to computations in the GW theory of curves with additional classes: the Euler classes of the (real) obstruction bundles. [PUBLICATION ABSTRACT]
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.
Author Lee, Junho
Parker, Thomas H.
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Snippet 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...
In a previous paper the authors defined symplectic ``Local Gromov-Witten invariants'' associated to spin curves and showed that the GW invariants of a K\"ahler...
In a previous paper the authors defined symplectic "Local Gromov-Witten invariants" associated to spin curves and showed that the GW invariants of a Kähler...
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SubjectTerms Algebra
Coordinate systems
Cylinders
Geometry
Linear algebra
Linearization
Mathematical manifolds
Mathematical vectors
Mathematics
Numerical analysis
Perceptron convergence procedure
Topological compactness
Vector spaces
Title AN OBSTRUCTION BUNDLE RELATING GROMOV-WITTEN INVARIANTS OF CURVES AND KÄHLER SURFACES
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