2021/06/02 by Shaoyun Bai, Bai, Shaoyun, Mohan Swaminathan +1
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2106.01206
openalex publication_date 2021/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define an integer-valued virtual count of embedded pseudo-holomorphic curves of two times a primitive homology class and arbitrary genus in symplectic Calabi--Yau 3-folds, which can be viewed as an extension of Taubes' Gromov invariant. The construction depends on a detailed study of bifurcations of moduli spaces of embedded pseudo-holomorphic curves which is partially motivated by Wendl's recent solution of Bryan--Pandharipande's super-rigidity conjecture.