轨形Riemann面的Gromov-Witten不变量沿光滑点的加权涨开公式

Weighted blow-up of Gromov-Witten invariants of orbifold Riemannian surfaces along smooth points

本文考虑当一个紧辛轨形(orbifold)Riemann面(X,ω)沿着光滑点作加权涨开时,它的轨形Gromov-Witten不变量的变化情形和辛一致规则(uniruledness)性质的变化情形;证明了如下的结果:<α_1,...,α_m>~X _g,A=<p*α_1,...,p*α_m,■,<α_1,...,α_m,[pt]>~X _g,A=I_A·■.第一个公式表明,当(X,ω)是辛一致规则的(uniruled)时,它的沿光滑点的加权涨开■也是辛一致规则的.

In this paper, we study the change of orbifold Gromov-Witten invariants, and the change of the symplectic uniruledness of a compact symplectic orbifold Riemannian surface under weighted blow-up along smooth points. We prove that The first formula shows that when （X, w） is symplectic uniruled, then so is （X, w）, the weighted blow up of （X, w） along smooth point.