Quantum cosmology of [CN/μr]

Arend Bayer; Charles Cadman

doi:10.1112/S0010437X10004793

Quantum cosmology of [C^N/μ_r]

Arend Bayer, Charles Cadman

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We give a construction of the moduli space of stable maps to the classifying stack Bμ_r of a cyclic group by a sequence of rth root constructions on (M)
over bar (0,n). We prove a closed formula for the total Chern class of μ_r-eigenspaces of the Hodge bundle, and thus of the obstruction bundle of the genus-zero Gromov–Witten theory of stacks of the form [C^N/μ_r]. We deduce linear recursions for genus-zero Gromov–Witten invariants.

Original language	English
Pages (from-to)	1291-1322
Number of pages	32
Journal	Compositio Mathematica
Volume	146
Issue number	5
DOIs	https://doi.org/10.1112/S0010437X10004793
Publication status	Published - Sept 2010

Keywords / Materials (for Non-textual outputs)

stable maps
root construction
Gromov–Witten invariants
stacks
quantum orbifold cohomology

Access to Document

10.1112/S0010437X10004793

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7881138

Cite this

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AB - 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 (M) over bar (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.

KW - stable maps

KW - root construction

KW - Gromov–Witten invariants

KW - stacks

KW - quantum orbifold cohomology

U2 - 10.1112/S0010437X10004793

DO - 10.1112/S0010437X10004793

M3 - Article

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VL - 146

SP - 1291

EP - 1322

JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 5