Degeneracy theorems for holomorphic mappings between algebraic varieties

Molzon, Robert

doi:10.1090/S0002-9947-1982-0642337-0

Degeneracy theorems for holomorphic mappings between algebraic varieties
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Trans. Amer. Math. Soc. 270 (1982), 183-192 Request permission

Abstract:

Degeneracy theorems are proved for holomorphic mappings from affine algebraic manifolds to projective algebraic manifolds of equal dimensions. A mapping is degenerate if it satisfies a growth estimate and omits a set of $\kappa$-plane sections of positive capacity; the capacity being defined in terms of a singular integral. The capacity is a more delicate method of measuring the size of a set of $\kappa$-plane sections than Hausdorff measure and arises naturally by considering the singular integrals in the First Main Theorem of Nevanlinna.

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