发表机构
School of Mathematics, Southwest Jiaotong University（西南交通大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明正则性定理，建立射影平面相对 Gromov-Witten 理论的 conifold 间隙，通过椭圆迹和差分恒等式将普通间隙转移至相对情形。
AI 中文摘要
Conifold 边界条件约束了高亏格拓扑弦自由能，但次主导极点的消除并非由其主导奇异行为所蕴含。我们证明了连通椭圆完整循环迹的正则性定理，并利用它建立了带光滑三次边界及顶部 Hodge 类插入的射影平面最大接触相对 Gromov-Witten 理论的 Nekrasov-Shatashvili conifold 间隙。高亏格局部/相对对应将普通势用相对势及微分后的低亏格贡献表达。我们将其 conifold 极化修正识别为椭圆迹。一个中心差分恒等式将每个非真空配分权重重新求和为内容乘积乘以正则指数。对于输入势的任意正则部分及任何具有简单零点的 nome，归一化的非真空连通贡献可被 conifold 坐标及耦合常数平方整除。因此，整个极部分和有限部分由真空常数决定。三角归纳将已知的普通局部射影平面间隙转移到相对理论。我们还获得了有限部分恒等式、正则 Taylor 系数的有限公式以及全纯歧义的 reconstruction。该论证在耦合常数意义下是形式的，并在每个固定亏格给出全纯余项。
英文摘要
Conifold boundary conditions constrain higher genus topological string free energies, but the cancellation of subleading poles is not implied by their leading singular behavior. We prove a regularity theorem for connected elliptic completed cycle traces and use it to establish the Nekrasov-Shatashvili conifold gap for the maximal contact relative Gromov-Witten theory of the projective plane with a smooth cubic boundary and a top Hodge class insertion. The higher genus local/relative correspondence expresses the ordinary potential in terms of the relative potential and differentiated lower genus contributions. We identify its conifold polarized correction with an elliptic trace. A central difference identity resums each non-vacuum partition weight into a content product multiplied by a regular exponential. For arbitrary regular parts of the input potentials and any nome with a simple zero, the normalized non-vacuum connected contribution is divisible by the conifold coordinate and by the square of the coupling. The entire polar part and finite part are consequently determined by the vacuum constants. A triangular induction transfers the known ordinary local projective plane gap to the relative theory. We also obtain finite part identities, finite formulas for regular Taylor coefficients, and reconstruction of the holomorphic ambiguities. The argument is formal in the coupling and gives holomorphic remainders at every fixed genus.
Comments21 pages
