Degeneracy theorems for holomorphic mappings between algebraic varieties

Author:
Robert Molzon

Journal:
Trans. Amer. Math. Soc. **270** (1982), 183-192

MSC:
Primary 32H30

DOI:
https://doi.org/10.1090/S0002-9947-1982-0642337-0

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 -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 -plane sections than Hausdorff measure and arises naturally by considering the singular integrals in the First Main Theorem of Nevanlinna.

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DOI:
https://doi.org/10.1090/S0002-9947-1982-0642337-0

Article copyright:
© Copyright 1982
American Mathematical Society