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Comparing virtual fundamental classes: gauge theoretical Gromov-Witten invariants for toric varieties


Okonek, C; Teleman, A (2003). Comparing virtual fundamental classes: gauge theoretical Gromov-Witten invariants for toric varieties. Asian Journal of Mathematics, 7(2):167-198.

Abstract

In general, a Kobayashi-Hitchin correspondence establishes an isomorphism between a moduli space of stable algebraic geometric objects and a moduli space of solutions of a certain (generalized) Hermite-Einstein equation. We believe that, for a large class of moduli problems, this correspondence respects the virtual fundamental classes defined in the two categories.
We prove this statement in an interesting case, namely the moduli problem associated with the symplectic factorization problem which yields the complete toric varieties. Therefore, our main objects are the moduli spaces of "twisted" linear sigma models associated with this symplectic factorization problem. We describe these moduli spaces in both gauge theoretic and algebraic geometric frameworks and we identify the correponding virtual fundamental classes.

Abstract

In general, a Kobayashi-Hitchin correspondence establishes an isomorphism between a moduli space of stable algebraic geometric objects and a moduli space of solutions of a certain (generalized) Hermite-Einstein equation. We believe that, for a large class of moduli problems, this correspondence respects the virtual fundamental classes defined in the two categories.
We prove this statement in an interesting case, namely the moduli problem associated with the symplectic factorization problem which yields the complete toric varieties. Therefore, our main objects are the moduli spaces of "twisted" linear sigma models associated with this symplectic factorization problem. We describe these moduli spaces in both gauge theoretic and algebraic geometric frameworks and we identify the correponding virtual fundamental classes.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:gauge theoretical Gromov-Witten invariants; Kobayashi-Hitchin correspondence; virtual fundamental class; toric varieties
Language:English
Date:2003
Deposited On:29 Nov 2010 16:26
Last Modified:05 Apr 2016 13:25
Publisher:International Press
ISSN:1093-6106
Additional Information:© 2003 International Press
Official URL:http://www.intlpress.com/AJM/AJM-v07.php#AJM-7-2
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1084.53020
http://www.ams.org/mathscinet-getitem?mr=2014963

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