A mirror theorem for multi-root stacks and applications

Hsian-Hua Tseng ^[1] ; Fenglong You ^[2]
1. [1] Ohio State University
  
  Ohio State University
  
  City of Columbus, Estados Unidos
2. [2] Swiss Federal Institute of Technology in Zurich
  
  Swiss Federal Institute of Technology in Zurich
  
  Zürich, Suiza
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 1, 2023
Idioma: inglés
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Resumen
- Let X be a smooth projective variety with a simple normal crossing divisor D:=D1+D2+⋯+Dn, where Di ⊂ X are smooth, irreducible and nef. We prove a mirror theorem for multi-root stacks XD,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 XD,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 XD,r→ .