2005/05/05 by Chien‐Hao Liu, Chien-Hao Liu, Shing-Tung Yau +3
Mathematics · Physics and Astronomy · #14N35 #53D45 #81T30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Finite Group Theory Research #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Symplectic Geometry (math.SG) #hep-th #math.AG #math.SG #msc:14N35 #msc:53D45 #msc:81T30
paper · pdf · doi:10.48550/arxiv.math/0505084
38+2 pages, 5 figures
arxiv created 2005/05/05 · openalex publication_date 2005/05/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 gauge 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.