Bifurcations of embedded curves and toward an extension of Taubes’s Gromov invariant to Calabi–Yau 3-folds

Abstract

We define an integer-valued virtual count of embedded pseudoholomorphic 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’s Gromov invariant. The construction depends on a detailed study of bifurcations of moduli spaces of embedded pseudoholomorphic curves which is partially motivated by Wendl’s recent solution of Bryan and Pandharipande’s superrigidity conjecture.