Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 32H30

Retrieve articles in all journals with MSC: 32H30


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1982-0642337-0
Article copyright: © Copyright 1982 American Mathematical Society