Gromov-Witten theory of root gerbes. I: Structure of genus 0 moduli spaces

DOI10.4310/JDG/1418345536zbMATH Open1326.14130arXiv0907.2087OpenAlexW2962728730WikidataQ115168265 ScholiaQ115168265MaRDI QIDQ2255312

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Publication date: 9 February 2015

Published in: (Search for Journal in Brave)

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

Full work available at URL: https://arxiv.org/abs/0907.2087

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