Multi-point virtual structure constants and mirror computation of CP²-model

In this paper, we propose a geometrical approach to mirror computation of genus 0 Gromov-Witten invariants of CP². We use multipoint virtual structure constants, which are defined as intersection numbers of a compact moduli space of quasi-maps from CP¹ to CP² with 2 + n marked points. We conjecture that some generating functions of them produce mirror map and the others are translated into generating functions of Gromov-Witten invariants via the mirror map. We generalize this formalism to open string case. In this case, we have to introduce infinite number of deformation parameters to obtain results that agree with some known results of open Gromov-Witten invariants of CP². We also apply multi-point virtual structure constants to compute closed and open Gromov-Witten invariants of a non-nef hypersurface in projective space. This application simplifies the computational process of generalized mirror transformation.