Geometrical Proof of Generalized Mirror Transformation for Multi-Point Virtual Strucutre Constants of Projective Hypersurfaces
Masao Jinzenji
TL;DR
This work provides a geometric proof of the generalized mirror transformation for multi-point virtual structure constants associated with degree $k$ hypersurfaces in $CP^{N-1}$. It develops a refined moduli space framework for quasimaps, resolves evaluation-map discontinuities by passing to the stack $C^N/C^{\times}$, and identifies new excess intersections that drive the multi-point corrections. The main result expresses multi-point $w$-invariants in terms of genus-zero Gromov-Witten invariants plus structured excess contributions, via a detailed combinatorial decomposition and perturbation analysis. The findings establish a rigorous geometric basis for multi-point mirror symmetry and clarify the role of excess intersections in CY and higher-point settings.
Abstract
In this paper, we propose a geometric proof of the generalized mirror transformation for multi-point virtual structure constants of degree k hypersurfaces in CP^{N-1}.