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Transactions of the American Mathematical Society

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Degeneracy theorems for holomorphic mappings between algebraic varieties

Author: Robert Molzon
Journal: Trans. Amer. Math. Soc. 270 (1982), 183-192
MSC: Primary 32H30
MathSciNet review: 642337
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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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Article copyright: © Copyright 1982 American Mathematical Society