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Intrinsic pseudo-volume forms for logarithmic pairs

Thomas Dedieu (2010)

Bulletin de la Société Mathématique de France

We study an adaptation to the logarithmic case of the Kobayashi-Eisenman pseudo-volume form, or rather an adaptation of its variant defined by Claire Voisin, for which she replaces holomorphic maps by holomorphic K -correspondences. We define an intrinsic logarithmic pseudo-volume form Φ X , D for every pair ( X , D ) consisting of a complex manifold X and a normal crossing Weil divisor D on X , the positive part of which is reduced. We then prove that Φ X , D is generically non-degenerate when X is projective and K X + D ...

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