Gromov-Witten Theory of Spin Curves and Orbifolds
About this Volume
Edited by: Tyler J. Jarvis, Takashi Kimura and Arkady Vaintrob
2006: Volume: 403
ISBNs: 978-0-8218-3534-0 (print); 978-0-8218-7993-1 (online)
This volume is a collection of articles on orbifolds, algebraic curves with higher spin structures, and related invariants of Gromov-Witten type. Orbifold Gromov-Witten theory generalizes quantum cohomology for orbifolds, whereas spin cohomological field theory is based on the moduli spaces of higher spin curves and is related by Witten's conjecture to the Gelfand-Dickey integrable hierarchies.
A common feature of these two very different looking theories is the central role played by orbicurves in both of them. Insights in one theory can often yield insights into the other. This book brings together for the first time papers related to both sides of this interaction. The articles in the collection cover diverse topics, such as geometry and topology of orbifolds, cohomological field theories, orbifold Gromov-Witten theory, $G$-Frobenius algebra and singularities, Frobenius manifolds and Givental's quantization formalism, moduli of higher spin curves and spin cohomological field theory.
Graduate students and research mathematicians interested in algebraic geometry, topology, and mathematical physics.
Table of Contents
- A. Polishchuk – Moduli spaces of curves with effective $r$-spin structures
- Alessandro Chiodo – A construction of Witten’s top Chern class in $K$-theory
- Y.-P. Lee – Witten’s conjecture and the Virasoro conjecture for genus up to two
- Xiaobo Liu – Idempotents on the big phase space
- Ralph M. Kaufmann – Singularities with symmetries, orbifold Frobenius algebras and mirror symmetry
- Yongbin Ruan – The cohomology ring of crepant resolutions of orbifolds
- Ernesto Lupercio and Bernardo Uribe – Differential characters on orbifolds and string connections. I. Global quotients
- Jack Morava – HKR characters and higher twisted sectors
- S. V. Shadrin – Combinatorics of binomial decompositions of the simplest Hodge integrals
- James Spencer – The orbifold cohomology of the moduli of genus-two curves