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

الأصل · EN

Let X be a smooth complex projective algebraic variety. Given a line bundle L over X and an integer r>1 one defines the stack √[r]L/X of r-th roots of L. Motivated by Gromov-Witten theoretic questions, in this paper we analyze the structure of moduli stacks of genus 0 twisted stable maps to √[r]L/X. Our main results are explicit constructions of moduli stacks of genus 0 twisted stable maps to √[r]L/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 √[r]L/X in terms of those of X.