Un théoréme de Nakai-Moishezon pour certaines classes de type (1,1)

Original · EN

Let X be a smooth compact projective variety over C. Let H²(π₁(X),R)¹,¹ be the intersection of H¹,¹(X,R) with the image of the map H²(π₁(X),R)→ H²(X) induced by the classifying map X→ Bπ₁(X). Let NS(X) be the Néron-Severi group of X. Let [ω]∈ H²(π₁(X),R)¹,¹+ NS(X)⊗ R. In this note, we prove that [ω] is the cohomology class of a Kähler metric if and only if for every d-dimensional reduced closed algebraic subvariety Z⊂ X, [ω]ᵈ.Z>0.