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 subset of X are smooth, irreducible and nef. We prove a mirror theorem for multi-root stacks X-D,X-(r) over right arrow 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,X-(r) over right arrow stabilize for sufficiently large (r) over right arrow. (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,X-(r) over right arrow.
Selecta Mathematica. N.S., 29 (1)
ISSN:1420-9020
ISSN:1022-1824