Research Papers

Home Publications Research Papers

Abstract: This is the first in a series of papers on counting surfaces on Calabi-Yau 4-folds. To complement the Hilbert scheme of 2-dimensional subschemes, we introduce two types of moduli spaces of stable pairs. We show that all three moduli spaces are related by GIT wall-crossing and parametrize stable objects in the bounded derived category. We construct reduced Oh-Thomas virtual cycles on the moduli spaces via Kiem-Li cosection localization and prove that they are deformation invariant along Hodge loci. As an application, we show that the variational Hodge conjecture holds for any family of Calabi-Yau 4-folds supporting a nonzero reduced virtual cycle.

List