The mixed spin P-fields （MSP for short） theory sets up a geometric platform to relate Gromov-Witten invariants of the quintic three-fold and Fan-Jarvis-Ruan-Witten invariants of the quintic polynomial in five variab...The mixed spin P-fields （MSP for short） theory sets up a geometric platform to relate Gromov-Witten invariants of the quintic three-fold and Fan-Jarvis-Ruan-Witten invariants of the quintic polynomial in five variables. It starts with Wittens vision and the P-fields treatment of GW invariants and FJRW invaxiants. Then it briefly discusses the master space technique and its application to the set-up of the MSP moduli. Some key results in MSP theory are explained and some examples are provided.展开更多
We prove a conjectural formula of Maulik-Pandharipande on the degree one and two GW invariants of a surface with a smooth canonical divisor.We use the method of degeneration and the localized GW invariants introduced ...We prove a conjectural formula of Maulik-Pandharipande on the degree one and two GW invariants of a surface with a smooth canonical divisor.We use the method of degeneration and the localized GW invariants introduced by the authors.展开更多
Let S be a smooth algebraic surface and let L be a line bundle on S.Suppose there is a holomorphic two form over S with zero loci to be a curve C.We show that the DonaldsonThomas invariant of the P^1 scroll X = P（L＋...Let S be a smooth algebraic surface and let L be a line bundle on S.Suppose there is a holomorphic two form over S with zero loci to be a curve C.We show that the DonaldsonThomas invariant of the P^1 scroll X = P（L＋Бs） vanishes unless the curves being enumerated lie in D = P（L︱C＋БC）.Our method is cosection localization of Y.-H.Kiem and J.Li.展开更多
基金supported by Hong Kong General Research Fund(Nos.600711,6301515,602512)the National Science Foundation(Nos.NSF-1104553,DMS-1159156,DMS-1206667,DMS-1159416)
文摘The mixed spin P-fields （MSP for short） theory sets up a geometric platform to relate Gromov-Witten invariants of the quintic three-fold and Fan-Jarvis-Ruan-Witten invariants of the quintic polynomial in five variables. It starts with Wittens vision and the P-fields treatment of GW invariants and FJRW invaxiants. Then it briefly discusses the master space technique and its application to the set-up of the MSP moduli. Some key results in MSP theory are explained and some examples are provided.
基金support from NRFsupported by an NSF granta DARPA grant
文摘We prove a conjectural formula of Maulik-Pandharipande on the degree one and two GW invariants of a surface with a smooth canonical divisor.We use the method of degeneration and the localized GW invariants introduced by the authors.
基金Partially supported by Hong Kong GRF(Grant No.600711)
文摘Let S be a smooth algebraic surface and let L be a line bundle on S.Suppose there is a holomorphic two form over S with zero loci to be a curve C.We show that the DonaldsonThomas invariant of the P^1 scroll X = P（L＋Бs） vanishes unless the curves being enumerated lie in D = P（L︱C＋БC）.Our method is cosection localization of Y.-H.Kiem and J.Li.
