The genus-one global mirror theorem for the quintic $3$-fold. (May 2019)

• Record Type: Journal Article
• Authors: Guo, Shuai; Ross, Dustin
• Is Part Of: Compositio mathematica. Volume 155:Number 5(2019)
• Page Start: 995
• Page End: 1024
• Publication Date: 2019-05
• Subjects: 14N35, -- 53D45, -- 53D37 (primary); mirror symmetry, -- Gromov–Witten theory, -- Fan–Jarvis–Ruan–Witten theory; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X19007231
• Languages: English
• ISSNs: 0010-437X

Abstract

Abstract : We prove the genus-one restriction of the all-genus Landau–Ginzburg/Calabi–Yau conjecture of Chiodo and Ruan, stated in terms of the geometric quantization of an explicit symplectomorphism determined by genus-zero invariants. This gives the first evidence supporting the higher-genus Landau–Ginzburg/Calabi–Yau correspondence for the quintic $3$ -fold, and exhibits the first instance of the 'genus zero controls higher genus' principle, in the sense of Givental's quantization formalism, for non-semisimple cohomological field theories.