发表机构
Southwest Jiaotong University（西南交通大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究 Calabi-Yau 三维流形翻折的局部 Gromov-Witten 差分方程，提出用中心差分算子组织本原次数，证明经典强迫项决定 GV 谱，并揭示重构失败的三种情形。
AI 中文摘要
我们研究了 Calabi-Yau 三维流形中可收缩有理曲线的局部 Gromov-Witten 理论中差分方程所编码的信息。从 Bryan-Katz-Leung 多重覆盖分解出发，我们通过一个与例外射线支撑的最大公约数相关联的中心差分算子，将所有非零本原次数组织在一条例外射线上。所得方程由显式的 Fejér 型 Laurent 核控制。我们的主要结构结果表明，一旦例外射线及其格归一化被固定，完整的量子强迫项、其在 λ=0 处的经典特化以及局部亏格零 Gopakumar-Vafa 谱相互决定。特别地，经典强迫项已经通过显式的除数反演决定了每个局部 GV 重数。因此，量子差分方程携带一个非平凡的平移轮廓，但这一额外的 λ 依赖性不包含关于亏格零 GV 谱的进一步信息。对于有限支撑，我们进一步引入了最细公共平移格，并确定了关于可除性的最小 Laurent 多项式分母清除算子。其分圆因子分解定义了局部枚举理论的严格更粗的阴影。显式的长度二、E6、E7 和 E8 翻折模型展示了三种不同的重构失败：相同的 Kollár 长度可以给出不同的强迫项，不同的 GV 支撑可以具有相同的分圆骨架，且相同的局部差分数据不一定决定翻折的解析类型。这些结果给出了局部 Gromov-Witten 差分方程所保留的几何和枚举信息的精确层级。
英文摘要
We study difference equations for the local Gromov-Witten theory of a contractible rational curve in a Calabi-Yau threefold from the viewpoint of reconstruction. Starting from the Bryan-Katz-Leung multiple cover decomposition, we associate to all nonzero local GV degree sectors on an exceptional ray a single central difference forcing term governed by explicit Fejér-type Laurent kernels. Our main result is an information equivalence theorem: once the exceptional ray and its lattice normalization are fixed, the full quantum forcing, its regular specialization at $λ=0$, and the local genus zero Gopakumar-Vafa spectrum determine one another. In particular, every local GV multiplicity is recovered from the classical forcing by an explicit Möbius inversion. In the primitive normalization relevant to a simple flopping contraction, the same classical forcing also recovers the noncommutative and commutative widths of the contraction algebra: the former is the order at $q=1$ of the exponentiated forcing and the latter is its first $q$-coefficient. For finite support we further determine the minimal Laurent polynomial denominator clearing operator on the finest common shift lattice. Its cyclotomic factorization is strictly coarser than the GV spectrum. Length two, $E_6$, $E_7$, and $E_8$ examples exhibit the resulting hierarchy of information loss: Kollár length does not determine the forcing, the cyclotomic skeleton does not determine the GV support, and even the complete local difference data do not determine the analytic type of the flop.
Comments20 pages. Revised title and exposition. The reconstruction theorem is foregrounded; a contraction algebra interpretation of the classical forcing is added; the relation to quantum K-theoretic q-difference/reconstruction literature is clarified
