Deformation limits of projective manifolds: Hodge numbers and strongly Gauduchon metrics

Product of generalized p-Kähler manifolds

“…1K ⇐⇒ b 1 is even ( [17]) ⇐⇒ 1S ( [14], Lemme II.3, or [21], p. 18) (in [16], Proposition 25, the authors proved that 1S ⇐⇒ 1WK). The Hopf surface is not in this class.…”

Pluripotential theory on compact Hermitian manifolds

“…A strengthened version of the Gauduchon condition was considered by Popovici in [47]: Definition 2.6. (strongly Gauduchon metric).…”

“…Of course strongly Gauduchon implies Gauduchon and these notions coincide if the ∂∂-lemma holds on X (see [47]) but in general the inclusion is strict. Note also that any balanced metric is strongly Gauduchon.…”

“…The strongly Gauduchon condition was introduced by Popovici in [47] in connection with studies of deformation limits of projective or Kähler manifolds. We refer to [47] for the geometric conditions imposed by this structure.…”

“…We refer to [47] for the geometric conditions imposed by this structure. In particular a necessary and sufficient condition of existence of such a metric on a manifold X is the nonexistence of a positive d-exact (1, 1) current on X.…”