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1 November 2002 Absolute and relative Gromov-Witten invariants of very ample hypersurfaces
Andreas Gathmann
Duke Math. J. 115(2): 171-203 (1 November 2002). DOI: 10.1215/S0012-7094-02-11521-X

Abstract

For any smooth complex projective variety $X$ and any smooth very ample hypersurface $Y\subset X$, we develop the technique of genus zero relative Gromov-Witten invariants of $Y$ in $X$ in algebro-geometric terms. We prove an equality of cycles in the Chow groups of the moduli spaces of relative stable maps which relates these relative invariants to the Gromov-Witten invariants of $X$ and $Y$. Given the Gromov-Witten invariants of $X$, we show that these relations are sufficient to compute all relative invariants, as well as all genus zero Gromov-Witten invariants of $Y$ whose homology and cohomology classes are induced by $X$.

Citation

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Andreas Gathmann. "Absolute and relative Gromov-Witten invariants of very ample hypersurfaces." Duke Math. J. 115 (2) 171 - 203, 1 November 2002. https://doi.org/10.1215/S0012-7094-02-11521-X

Information

Published: 1 November 2002
First available in Project Euclid: 26 May 2004

zbMATH: 1042.14032
MathSciNet: MR1944571
Digital Object Identifier: 10.1215/S0012-7094-02-11521-X

Subjects:
Primary: 14N35
Secondary: 14H10 , 14J70 , 14N10

Rights: Copyright © 2002 Duke University Press

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Vol.115 • No. 2 • 1 November 2002
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