|Date||May 23, 2022|
The Oh-Thomas virtual cycle generally vanishes when applied to surface classes on Calabi-Yau 4-folds. Using methods of Kiem-Li and Kiem-Park, we reduce the Oh-Thomas obstruction theory by H^31-forms in order to obtain non-trivial invariants. On the semi-regular locus of the moduli space, our reduced virtual cycle coincides with the fundamental class. In a smooth family of Calabi-Yau 4-folds, we prove deformation invariance along the Hodge locus. Joint work with Y. Bae and H. Park.