Holomorphic curves on algebraic varieties pdf

By an entire curve we mean a non constant holomorphic map f. Recent results on jet differentials and entire holomorphic. Pages 255267 from volume 169 2009, issue 1 by min ru. Lemma on logarithmic derivatives and holomorphic curves in. In this paper, we refine the concept of subgeneral position by introducing the notion of the index of subgeneral position. On holomorphic curves in algebraic varieties with ample irregularity. Holomorphic curves into algebraic varieties intersecting moving. This paper establishes a defect relation for algebraically nondegenerate holomorphic. Pdf spaces of holomorphic maps from cp1 to complex. Holomorphic curves into algebraic varieties annals of. Holomorphic curves in algebraic varieties of maximal.

Holomorphic curves in algebraic varieties of maximal albanese dimension katsutoshi yamanoi department of mathematics, graduate school of science. Spaces of holomorphic maps from cp1 to complex grassmann manifolds. Multivariable holomorphic functions let u be an open. Anti holomorphic multiplication and a real algebraic modular variety goresky, mark and tai, yung sheng, journal of differential geometry, 2003. Request pdf holomorphic curves into algebraic varieties intersecting moving hypersurface targets in ann. On holomorphic curves in algebraic varieties with ample irregularity takushiro ochiai 1 inventiones mathematicae volume 43, pages 83 96 1977 cite this article. The complex algebraic geometry is the overlap of the complex geometry and algebraic geometry.

The purpose of this paper is to prove the algebraic degeneracy of entire holomorphic curves into a normal algebraic variety xcarrying a nite map onto a semiabelian variety by assuming only some nonsingular part of xto be of loggeneral type see theorem 1. Pdf document information annals of mathematics fine hall washington road princeton university princeton, nj 08544, usa phone. Let x be a projective algebraic manifold of dimension m with irregularity 4 m. C x from the complex plane c into a complex algebraic normal variety x of positive log kodaira dimension that admits a.

We apply a technique introduced in 7 to holomorphic curves into an algebraic variety whose irregularity is greater than its dimension and establish the second main theorem. Yamanoi, the second main theorem for holomorphic curves into semiabelian varieties ii. Holomorphic curves into algebraic varieties intersecting moving hypersurface targets. Holomorphic curves into algebraic varieties intersecting divisors in. With this new notion we give some surprising improvement of the previous known second main.

Pdf in this paper, we first give a slight improvement of yamanois truncated second main theorem for holomorphic maps into abelian varieties. Holomorphic curves into algebraic varieties annals of mathematics. On holomorphic curves in algebraic varieties with ample. Nevanlinna theory, second main theorem, holomorphic curve, subgeneral position, index, schmidts subspace theorem. Entire holomorphic curves in algebraic varieties and nevanlinna theory japanese, sugaku 59 no. Holomorphic curves into algebraic varieties by min ru abstract this paper establishes a defect relation for algebraically nondegenerate holomorphic mappings into an arbitrary nonsingular complex projective variety v rather than just the projective space intersecting possible nonlinear hypersurfaces, extending the result of h. Degeneracy of holomorphic curves into algebraic varieties. The proof gives a simpli cation of that of the degeneracy theorem in 5.

Holomorphic curves in algebraic varieties project euclid. Degeneracy of holomorphic curves into algebraic varieties ii. Elliptic curves an elliptic curve is a smooth plane cubic curve e, that is, the set of points in the complex projective plane p2where a homogeneous polynomial of degree 3 in 3 variables vanishes smoothness is then equivalent to the fact that the partial derivatives of this polynomial have no common zero. On nevanlinna theory for holomorphic curves in abelian varieties yamanoi, katsutoshi, 2004. C v in a complex projective algebraic smooth variety v and making. Recently, there are many developments on the second main theorem for holomorphic curves into algebraic varieties intersecting divisors in general position or subgeneral position. Holomorphic curves into algebraic varieties intersecting. Deficiencies of holomorphic curves in algebraic varieties aihara, yoshihiro, tohoku mathematical journal, 2012. Lemma on logarithmic derivatives and holomorphic curves in algebraic varieties. Pdf uniqueness of holomorphic curves into abelian varieties.