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

Masao Jinzenji, Masahide Shimizu

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)411-468
Number of pages58
JournalCommunications in Number Theory and Physics
Issue number3
Publication statusPublished - 2013
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Mathematical Physics
  • Physics and Astronomy(all)


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