AI 中文总结
该研究为复射影平面的初等格罗莫夫-威滕不变量，在每个固定亏格下建立了完整大度渐近展开式，采用奇点分析等方法完成证明，是相关系列研究的首篇论文。
AI 中文摘要
本文是关于大度格罗莫夫-威滕不变量渐近行为系列论文的第一部分。我们证明了复射影平面的初等格罗莫夫-威滕不变量在每个固定亏格下的完整大度渐近展开式。证明采用奇点分析，将生成函数在主导奇点处的局部展开式转化为格罗莫夫-威滕不变量的渐近展开式。亏格为0的渐近展开式通过对Witten-Dijkgraaf-Verlinde-Verlinde（WDVV）方程的分析得到，更高亏格情形则通过半单上同调场论的Givental-Teleman重构定理及R矩阵作用的图和公式得到。
英文摘要
This is the first part of a series of papers on the large-degree asymptotics of Gromov--Witten invariants. In this paper, we prove complete large-degree asymptotic expansions, at every fixed genus, for the primary Gromov--Witten invariants of the complex projective plane. The proof uses singularity analysis to transfer the local expansions of generating functions at their dominant singularities to asymptotic expansions of Gromov--Witten invariants. The genus-zero asymptotic expansion is obtained from an analysis of the Witten--Dijkgraaf--Verlinde--Verlinde (WDVV) equation. The higher-genus cases are obtained from the Givental--Teleman reconstruction theorem for semisimple cohomological field theories and from the graph-sum formula for the $R$-matrix action.
Comments28 pages; no figures
