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
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.
