We define a formal Gromov-Witten theory of the quintic threefold via localization onℙ4.Our main result is a direct geometric proof of holomorphic anomaly equa-tions for the formal quintic in precisely the same form as...We define a formal Gromov-Witten theory of the quintic threefold via localization onℙ4.Our main result is a direct geometric proof of holomorphic anomaly equa-tions for the formal quintic in precisely the same form as predicted by B-model physics for the true Gromov-Witten theory of the quintic threefold.The results sug-gest that the formal quintic and the true quintic theories should be related by trans-formations which respect the holomorphic anomaly equations.Such a relationship has been recently found by Q.Chen,S.Guo,F.Janda,and Y.Ruan via the geometry of new moduli spaces.展开更多
In this paper,we study the higher genus FJRW theory of Fermat cubic singularity with maximal group of diagonal symmetries using Giventai formalism.As results,we prove the finite generation property and holomorphic ano...In this paper,we study the higher genus FJRW theory of Fermat cubic singularity with maximal group of diagonal symmetries using Giventai formalism.As results,we prove the finite generation property and holomorphic anomaly equation for the associated FJRW theory.Via general LG-LG mirror theorem,our results also hold for the Saito-Givental theory of the Fermat cubic singularity.展开更多
基金supported by SNF-200020182181,ERC-2012-AdG-320368-MCSK,ERC-2017-AdG-786580-MACI,SwissMAPthe Einstein Stiftung.H.L.was supported by the Grants ERC-2012-AdG-320368-MCSK and ERC-2017-AdG-786580-MACIfunding from the European Research Council(ERC)under the European Union’s Horizon 2020 research and innovation programme(grant agreement No 786580).
文摘We define a formal Gromov-Witten theory of the quintic threefold via localization onℙ4.Our main result is a direct geometric proof of holomorphic anomaly equa-tions for the formal quintic in precisely the same form as predicted by B-model physics for the true Gromov-Witten theory of the quintic threefold.The results sug-gest that the formal quintic and the true quintic theories should be related by trans-formations which respect the holomorphic anomaly equations.Such a relationship has been recently found by Q.Chen,S.Guo,F.Janda,and Y.Ruan via the geometry of new moduli spaces.
基金Supported by National Science Foundation of China(Grant No.11601279)National Science Foundation of China(Grant No.12071255)。
文摘In this paper,we study the higher genus FJRW theory of Fermat cubic singularity with maximal group of diagonal symmetries using Giventai formalism.As results,we prove the finite generation property and holomorphic anomaly equation for the associated FJRW theory.Via general LG-LG mirror theorem,our results also hold for the Saito-Givental theory of the Fermat cubic singularity.
