We use the technique of Ruan(1999)and Li and Ruan(2001)to construct the virtual neighborhoods and show that the Gromov-Witten invariants can be defined as integrals over the top strata of the virtual neighborhoods.We ...We use the technique of Ruan(1999)and Li and Ruan(2001)to construct the virtual neighborhoods and show that the Gromov-Witten invariants can be defined as integrals over the top strata of the virtual neighborhoods.We prove that the invariants defined in this way satisfy all the axioms of Gromov-Witten invariants summarized by Kontsevich and Manin(1994).展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11890660,11821001,11890663,11871352 and 1196131001)。
文摘We use the technique of Ruan(1999)and Li and Ruan(2001)to construct the virtual neighborhoods and show that the Gromov-Witten invariants can be defined as integrals over the top strata of the virtual neighborhoods.We prove that the invariants defined in this way satisfy all the axioms of Gromov-Witten invariants summarized by Kontsevich and Manin(1994).
基金Supported by the National Key Basic Research and Development Program(Grant No.2006CB805905)National Natural Science Foundation of China(Grant Nos.10631050,11171235,11101129and11126228)+2 种基金the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20060610004)Relative Theory in the String Theory(Grant No.11071173/A010301)Program for New Century Excellent Talents in Ministry of Education(Grant No.10-0588)
文摘In this paper, we prove the interior regularity for the solution to the Abreu equation in any dimension assuming the existence of the C^0 estimate.
