Transformation of algebraic Gromov-Witten invariants of three-folds under flops and small extremal transitions, with an appendix from the stringy and the symplectic viewpoint
Transformation of algebraic Gromov-Witten invariants of three-folds under flops and small extremal transitions, with an appendix from the stringy and the symplectic viewpoint
复制标题
翻牌和小极值变换下三重代数 Gromov-Witten 不变量的变换，并附有弦和辛观点的附录
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发表时间：
2005
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通讯作者：
S. Yau
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作者：
Chien‐Hao Liu;S. Yau
从代数相对Gromov-Witten理论及其应用的最新发展出发，研究了在代数几何环境下，投射3重变换的Gromov-Witten不变量在标准翻转和小极值变换下的性质.这给出了维滕的跨壁公式的相关函数的后代非线性σ模型在相邻的几何相位的规范的线性σ模型和辛方法在早期的工作，李安民和阮永斌在同一个问题的代数几何帐户。附录中给出了从弦和辛观点的简要说明，以补充和比较正文中的讨论。
We study how Gromov-Witten invariants of projective 3-folds transform under a standard flop and a small extremal transition in the algebro-geometric setting from the recent development of algebraic relative Gromov-Witten theory and its applications. This gives an algebro-geometric account of Witten’s wall-crossing formula for correlation functions of the descendant nonlinear sigma model in adjacent geometric phases of a gauged linear sigma model and of the symplectic approach in an earlier work of An-Min Li and Yongbin Ruan on the same problem. A terse account from the stringy and the symplectic viewpoint is given in the appendix to complement and compare to the discussion in the main text.