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.
