A mirror theorem for multi-root stacks and applications.

Let X be a smooth projective variety with a simple normal crossing divisor D : = D 1 + D 2 + ⋯ + D n , where D i ⊂ X are smooth, irreducible and nef. We prove a mirror theorem for multi-root stacks X D , r → by constructing an I-function lying in a slice of Givental's Lagrangian cone for Gromov–Witten theory of multi-root stacks. We provide three applications: (1) We show that some genus zero invariants of X D , r → stabilize for sufficiently large r → . (2) We state a generalized local-log-orbifold principle conjecture and prove a version of it. (3) We show that regularized quantum periods of Fano varieties coincide with classical periods of the mirror Landau–Ginzburg potentials using orbifold invariants of X D , r → . [ABSTRACT FROM AUTHOR]