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January 2015 Gromov-Witten theory of root Gerbes I: Structure of genus 0 moduli spaces
Elena Andreini, Yunfeng Jiang, Hsian-Hua Tseng
J. Differential Geom. 99(1): 1-45 (January 2015). DOI: 10.4310/jdg/1418345536

Abstract

Let $X$ be a smooth complex projective algebraic variety. Given a line bundle $\mathcal{L}$ over $X$ and an integer $r \gt 1$, one defines the stack $\sqrt[r]{\mathcal{L} / X}$ of $r$-th roots of $\mathcal{L}$. Motivated by Gromov-Witten theoretic questions, in this paper we analyze the structure of moduli stacks of genus $0$ twisted stable maps to $\sqrt[r]{\mathcal{L} / X}$. Our main results are explicit constructions of moduli stacks of genus $0$ twisted stable maps to $\sqrt[r]{\mathcal{L} / X}$ starting from moduli stacks of genus $0$ stable maps to $X$. As a consequence, we prove an exact formula expressing genus $0$ Gromov-Witten invariants of $\sqrt[r]{\mathcal{L} / X}$ in terms of those of $X$.

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Elena Andreini. Yunfeng Jiang. Hsian-Hua Tseng. "Gromov-Witten theory of root Gerbes I: Structure of genus 0 moduli spaces." J. Differential Geom. 99 (1) 1 - 45, January 2015. https://doi.org/10.4310/jdg/1418345536

Information

Published: January 2015
First available in Project Euclid: 12 December 2014

zbMATH: 1326.14130
MathSciNet: MR3299821
Digital Object Identifier: 10.4310/jdg/1418345536

Rights: Copyright © 2015 Lehigh University

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Vol.99 • No. 1 • January 2015
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