We compute the Hodge numbers of the polarised(pure) variation of Hodge structure V = grn-1WRn-1f!Z of the Landau-Ginzburg model f:Y → C mirror-dual to a weighted projective space wPn in terms of a variant of Reid'...We compute the Hodge numbers of the polarised(pure) variation of Hodge structure V = grn-1WRn-1f!Z of the Landau-Ginzburg model f:Y → C mirror-dual to a weighted projective space wPn in terms of a variant of Reid's age function of the anticanonical cone over wPn.This implies,for instance,that wPn has canonical singularities if and only if hn-1,0V = 1.We state a conjectural formula for the Hodge numbers of general hypergeometric variations.We show that a general fibre of the Landau-Ginzburg model is birational to a Calabi-Yau variety if and only if a general anticanonical section of wP is Calabi-Yau.We analyse the 104 weighted 3-spaces with canonical singularities,and show that a general anticanonical section is not a K3 surface exactly in those 9 cases where a generic fibre of the Landau-Ginzburg model is an elliptic surface of Kodaira dimension 1.展开更多
Xn（d1,...,dr-1,dr.;w） and Xn（e1,...,er-1,dr;w） are two complex odd-dimensional smooth weighted complete intersections defined in a smooth weighted hypersurfaee
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
文摘We compute the Hodge numbers of the polarised(pure) variation of Hodge structure V = grn-1WRn-1f!Z of the Landau-Ginzburg model f:Y → C mirror-dual to a weighted projective space wPn in terms of a variant of Reid's age function of the anticanonical cone over wPn.This implies,for instance,that wPn has canonical singularities if and only if hn-1,0V = 1.We state a conjectural formula for the Hodge numbers of general hypergeometric variations.We show that a general fibre of the Landau-Ginzburg model is birational to a Calabi-Yau variety if and only if a general anticanonical section of wP is Calabi-Yau.We analyse the 104 weighted 3-spaces with canonical singularities,and show that a general anticanonical section is not a K3 surface exactly in those 9 cases where a generic fibre of the Landau-Ginzburg model is an elliptic surface of Kodaira dimension 1.
基金supported by National Natural Science Foundation of China(Grant No.11001195)supported by National Natural Science Foundation of China(Grant No.11026197)Seed Foundation of Tianjin University(Grant Nos.60302036,60302055)
文摘Xn（d1,...,dr-1,dr.;w） and Xn（e1,...,er-1,dr;w） are two complex odd-dimensional smooth weighted complete intersections defined in a smooth weighted hypersurfaee
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.
