A Defect Relation for Equidimensional Holomorphic Mappings Between Algebraic Varieties

1972 ◽  
Vol 95 (3) ◽  
pp. 557 ◽  
Author(s):  
James Carlson ◽  
Phillip Griffiths
Keyword(s):  
Holomorphic Mappings ◽  
Algebraic Varieties ◽  
Defect Relation

scholarly journals On singular sets of flat holomorphic mappings with isolated singularities

1978 ◽  
Vol 70 ◽  
pp. 47-80
Author(s):  
Hideo Omoto
Keyword(s):  
Algebraic Geometry ◽  
Singular Point ◽  
Critical Points ◽  
Euler Number ◽  
Holomorphic Mappings ◽  
Algebraic Varieties ◽  
Isolated Singularities ◽  
General Fiber ◽  
Singular Sets ◽  
Algebraic Maps

In [4] B. Iversen studied critical points of algebraic mappings, using algebraic-geometry methods. In particular when algebraic maps have only isolated singularities, he shows the following relation; Let V and S be compact connected non-singular algebraic varieties of dimcV = n, and dimc S = 1, respectively. Suppose f is an algebraic map of V onto S with isolated singularities. Then it follows thatwhere χ denotes the Euler number, μf(p) is the Milnor number of f at the singular point p, and F is the general fiber of f : V → S.

scholarly journals Algebraic degeneracy theorem for holomorphic mappings into smooth projective algebraic varieties

1981 ◽  
Vol 84 ◽  
pp. 209-218
Author(s):  
Yoshihiro Aihara ◽  
Seiki Mori
Keyword(s):  
General Position ◽  
Holomorphic Mapping ◽  
Holomorphic Mappings ◽  
Holomorphic Curve ◽  
Algebraic Varieties ◽  
Picard Theorem ◽  
Picard’S Theorem ◽  
Picard's Theorem ◽  
Algebraic Degeneracy

The famous Picard theorem states that a holomorphic mapping f: C → P1(C) omitting distinct three points must be constant. Borel [1] showed that a non-degenerate holomorphic curve can miss at most n + 1 hyperplanes in Pn(C) in general position, thus extending Picard’s theorem (n = 1). Recently, Fujimoto [3], Green [4] and [5] obtained many Picard type theorems using Borel’s methods for holomorphic mappings.

scholarly journals Holomorphic mapping into algebraic varieties of general type

1990 ◽  
Vol 120 ◽  
pp. 155-170 ◽  
Author(s):  
Peichu Hu
Keyword(s):  
Complex Manifold ◽  
General Type ◽  
Holomorphic Mapping ◽  
Holomorphic Mappings ◽  
Canonical Bundle ◽  
Algebraic Varieties ◽  
Algebraic Manifold

We will study holomorphic mappingsfrom a connected complex manifold M of dimension m to a projective algebraic manifold N of dimension n. Assume first that N is of general type, i.e.where KN→N is the canonical bundle of N. If KN is positive, then N is of general type.

scholarly journals Nevanlinna theory and holomorphic mappings between algebraic varieties

1973 ◽  
Vol 130 (0) ◽  
pp. 145-220 ◽  
Author(s):  
Phillip Griffiths ◽  
James King
Keyword(s):  
Nevanlinna Theory ◽  
Holomorphic Mappings ◽  
Algebraic Varieties

A defect relation for meromorphic maps on generalized p-parabolic manifolds intersecting hypersurfaces in complex projective algebraic varieties

2013 ◽  
Vol 56 (2) ◽  
pp. 551-574 ◽  
Author(s):  
Qi Han
Keyword(s):  
Algebraic Varieties ◽  
Defect Relation ◽  
Meromorphic Maps ◽  
Complex Projective

AbstractWe establish a defect relation for algebraically non-degenerate meromorphic maps over generalized p-parabolic manifolds that intersect hypersurfaces in smooth projective algebraic varieties, extending certain results of H. Cartan, L. Ahlfors, W. Stoll, M. Ru, P. M. Wong and Philip P. W. Wong and others.

Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

2017 ◽  
Author(s):  
Claire Voisin
Keyword(s):  
Recent Work ◽  
Chow Groups ◽  
Ring Structure ◽  
Complete Intersections ◽  
Algebraic Varieties ◽  
Chow Ring ◽  
Hodge Structures ◽  
Chow Rings ◽  
Geometric Methods ◽  
The Right

This book provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The book is intended for both students and researchers, and not only presents a survey of the geometric methods developed in the last thirty years to understand the famous Bloch-Beilinson conjectures, but also examines recent work by the author. It focuses on two central objects: the diagonal of a variety—and the partial Bloch-Srinivas type decompositions it may have depending on the size of Chow groups—as well as its small diagonal, which is the right object to consider in order to understand the ring structure on Chow groups and cohomology. An exploration of a sampling of recent works by the author looks at the relation, conjectured in general by Bloch and Beilinson, between the coniveau of general complete intersections and their Chow groups and a very particular property satisfied by the Chow ring of K3 surfaces and conjecturally by hyper-Kähler manifolds. In particular, the book delves into arguments originating in Nori's work that have been further developed by others.

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