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Quantum cohomology of [ℂN/μr]

Part of:Projective and enumerative geometryCurvesFamilies, fibrations

Published online by Cambridge University Press:  22 June 2010

Arend Bayer and
Charles Cadman
Arend Bayer
Affiliation:
Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, USA
Charles Cadman
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Rd, Vancouver, BC, Canada V6P 4M8
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Abstract

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We give a construction of the moduli space of stable maps to the classifying stack Bμr of a cyclic group by a sequence of rth root constructions on $\overline {M}_{0, n}$. We prove a closed formula for the total Chern class of μr-eigenspaces of the Hodge bundle, and thus of the obstruction bundle of the genus-zero Gromov–Witten theory of stacks of the form [ℂN/μr]. We deduce linear recursions for genus-zero Gromov–Witten invariants.

Keywords

stable mapsroot constructionGromov–Witten invariantsstacksquantum orbifold cohomology

MSC classification

Secondary:14D23: Stacks and moduli problems14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants14H10: Families, moduli (algebraic)

Information

Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 5 , September 2010, pp. 1291 - 1322
Copyright
Copyright © Foundation Compositio Mathematica 2010

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