In this paper, one considers the change of orbifold Gromov Witten invariants under weighted blow-up at smooth points. Some blow-up formula for Gromov-Witten invariants of sym- pleetic orbifolds is proved. These result...In this paper, one considers the change of orbifold Gromov Witten invariants under weighted blow-up at smooth points. Some blow-up formula for Gromov-Witten invariants of sym- pleetic orbifolds is proved. These results extend the results of manifolds case to orbifold case.展开更多
In this paper,we prove quasi-modularity property for the twisted Gromov–Witten theory of O(3)over P^2.Meanwhile,we derive its holomorphic anomaly equation.
We represent stationary descendant Cromov-Witten invariants of projective space, up to explicit combinatorial factors, by polynomials. One application gives the asymptotic behaviour of the large degree behaviour of st...We represent stationary descendant Cromov-Witten invariants of projective space, up to explicit combinatorial factors, by polynomials. One application gives the asymptotic behaviour of the large degree behaviour of stationary descendant Gromov-Witten invariants in terms of intersection numbers over the moduli space of curves. We also show that primary Gromov-Witten invariants are ＂virtual＂ stationary descendants and hence the string and divisor equations can be understood purely in terms of stationary invariants.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
In this paper, we study genus 0 equivariant relative Gromov Witten invariants of P1 whose corresponding relative stable maps are totally ramified over one point. For fixed number of marked points, we show that such in...In this paper, we study genus 0 equivariant relative Gromov Witten invariants of P1 whose corresponding relative stable maps are totally ramified over one point. For fixed number of marked points, we show that such invariants are piecewise polynomials in some parameter space. The parameter space can then be divided into polynomial domains, called chambers. We determine the difference of polynomials between two neighbouring chambers. In some special chamber, which we called the totally negative chamber, we show that such a polynomial can be expressed in a simple way. The chamber structure here shares some similarities to that of double Hurwitz numbers.展开更多
基金partially supported by NSFC(Grant Nos.11228101,11371381)
文摘In this paper, one considers the change of orbifold Gromov Witten invariants under weighted blow-up at smooth points. Some blow-up formula for Gromov-Witten invariants of sym- pleetic orbifolds is proved. These results extend the results of manifolds case to orbifold case.
基金Supported by NSFC(Grant No.11601279)by Shandong Provincial Natural Science Foundation,China(Grant No.ZR2016AQ05)
文摘In this paper,we prove quasi-modularity property for the twisted Gromov–Witten theory of O(3)over P^2.Meanwhile,we derive its holomorphic anomaly equation.
基金Supported by Australian Research Council(Grant No.DP1094328)
文摘We represent stationary descendant Cromov-Witten invariants of projective space, up to explicit combinatorial factors, by polynomials. One application gives the asymptotic behaviour of the large degree behaviour of stationary descendant Gromov-Witten invariants in terms of intersection numbers over the moduli space of curves. We also show that primary Gromov-Witten invariants are ＂virtual＂ stationary descendants and hence the string and divisor equations can be understood purely in terms of stationary invariants.
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.
文摘In this paper, we study genus 0 equivariant relative Gromov Witten invariants of P1 whose corresponding relative stable maps are totally ramified over one point. For fixed number of marked points, we show that such invariants are piecewise polynomials in some parameter space. The parameter space can then be divided into polynomial domains, called chambers. We determine the difference of polynomials between two neighbouring chambers. In some special chamber, which we called the totally negative chamber, we show that such a polynomial can be expressed in a simple way. The chamber structure here shares some similarities to that of double Hurwitz numbers.
