Stability of Strongly Gauduchon Manifolds under Modifications

Abstract

In our previous works on deformation limits of projective and Moishezon manifolds, we introduced and made crucial use of the notion of strongly Gauduchon metrics as a reinforcement of the earlier notion of Gauduchon metrics. Using direct and inverse images of closed positive currents of type $(1, \, 1)$ and regularisation, we now show that compact complex manifolds carrying strongly Gauduchon metrics are stable under modifications. This stability property, known to fail for compact K\"ahler manifolds, mirrors the modification stability of balanced manifolds proved by Alessandrini and Bassanelli.