Positive form

In complex geometry, the term positive form refers to several classes of real differential forms of Hodge type (p, p).

Real (p,p)-forms on a complex manifold M are forms which are of type (p,p) and real, that is, lie in the intersection :${\displaystyle \Lambda ^{p,p}(M)\cap \Lambda ^{2p}(M,{\mathbb {R}}).}$ A real (1,1)-form ${\displaystyle \omega }$ is called positive if any of the following equivalent conditions hold

In algebraic geometry, positive (1,1)-forms arise as curvature forms of ample line bundles (also known as positive line bundles). Let L be a holomorphic Hermitian line bundle on a complex manifold,

its complex structure operator. Then L is equipped with a unique connection preserving the Hermitian structure and satisfying

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