The genus-one global mirror theorem for the quintic 3-fold. (30th May 2019) - Guo, Shuai; Ross, Dustin
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.