In this paper, by using the de Rham model of Chen-Ruan cohomology, we define the relative Chen-Ruan cohomology ring for a pair of almost complex orbifold （G, H） with H being an almost sub-orbifold of G. Then we use ...In this paper, by using the de Rham model of Chen-Ruan cohomology, we define the relative Chen-Ruan cohomology ring for a pair of almost complex orbifold （G, H） with H being an almost sub-orbifold of G. Then we use the Gromov Witten invariants of G, the blow-up of G along H,to give a quantum modification of the relative Chen-Ruan cohomology ring H^R（G, H） when H is a compact symplectic sub-orbifold of the compact symplectic orbifold G.展开更多
In this paper,we consider double ramification cycles with orbifold targets.An explicit formula for double ramification cycles with orbifold targets,which is parallel to and generalizes the one known for the smooth cas...In this paper,we consider double ramification cycles with orbifold targets.An explicit formula for double ramification cycles with orbifold targets,which is parallel to and generalizes the one known for the smooth case,is provided.Some applications for orbifold Gromov–Witten theory are also included.展开更多
Consider a Hamiltonian action of S1 on （Cn^n＋1,ωstd）, we shown that the Hamiltonian Gromov-Witten invariants of it are well-defined. After computing the Hamiltonian Gromov-Witten invariants of it, we construct a r...Consider a Hamiltonian action of S1 on （Cn^n＋1,ωstd）, we shown that the Hamiltonian Gromov-Witten invariants of it are well-defined. After computing the Hamiltonian Gromov-Witten invariants of it, we construct a ring homomorphism from HS1,CR（X, R） to the small orbifold quantum cohomology of X//rS^1 and obtain a simpler formula of the Gromov-Witten invariants for weighted projective space.展开更多
The study of the moduli space plays an important role in classical enumerative geometry and its interaction with string theory in physics. Given X=[P1/Zr] and let x＇ = （[0]a , [∞]b） the 2-tuple of twisted sectors ...The study of the moduli space plays an important role in classical enumerative geometry and its interaction with string theory in physics. Given X=[P1/Zr] and let x＇ = （[0]a , [∞]b） the 2-tuple of twisted sectors on X , we construct in this paper two different compactifications of the moduli space M0,2（X, d[P1/Zr], x＇）： Nonlinear Sigma Model Mx＇d and Linear Sigma Model Nx＇d . Relations between Mx＇d and Nx＇d are studied and a new gluing recursive relation on Nx＇d is derived from Mx＇d due to virtual localization formula.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11071173 and 11221101)
文摘In this paper, by using the de Rham model of Chen-Ruan cohomology, we define the relative Chen-Ruan cohomology ring for a pair of almost complex orbifold （G, H） with H being an almost sub-orbifold of G. Then we use the Gromov Witten invariants of G, the blow-up of G along H,to give a quantum modification of the relative Chen-Ruan cohomology ring H^R（G, H） when H is a compact symplectic sub-orbifold of the compact symplectic orbifold G.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11890663,12071322,11890660,11826102)the National Key R&D Program of China(Grant No.2020YFA0714000)+1 种基金the Sichuan Science and Technology Program(Grant Nos.2019YJ0509 and 2022JDTD0019)a joint research project of Laurent Mathematics Research Center of Sichuan Normal University and V.C.&V.R.Key Lab of Sichuan Province。
文摘In this paper,we consider double ramification cycles with orbifold targets.An explicit formula for double ramification cycles with orbifold targets,which is parallel to and generalizes the one known for the smooth case,is provided.Some applications for orbifold Gromov–Witten theory are also included.
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.
基金partially supported by NSFC(Grant Nos.11021101 and 11426233)
文摘Consider a Hamiltonian action of S1 on （Cn^n＋1,ωstd）, we shown that the Hamiltonian Gromov-Witten invariants of it are well-defined. After computing the Hamiltonian Gromov-Witten invariants of it, we construct a ring homomorphism from HS1,CR（X, R） to the small orbifold quantum cohomology of X//rS^1 and obtain a simpler formula of the Gromov-Witten invariants for weighted projective space.
基金supported by Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20100181110071)National Natural Science Foundation of China (Grant No. 11071176),supported by National Natural Science Foundation of China (Grant Nos. 11071173 and 11221101)Hundred Talents Program for Young Teachers (Grant No. SWJTU12BR028)
文摘The study of the moduli space plays an important role in classical enumerative geometry and its interaction with string theory in physics. Given X=[P1/Zr] and let x＇ = （[0]a , [∞]b） the 2-tuple of twisted sectors on X , we construct in this paper two different compactifications of the moduli space M0,2（X, d[P1/Zr], x＇）： Nonlinear Sigma Model Mx＇d and Linear Sigma Model Nx＇d . Relations between Mx＇d and Nx＇d are studied and a new gluing recursive relation on Nx＇d is derived from Mx＇d due to virtual localization formula.
