The goal of this e-book is to supply a entire account of upper dimensional Nevanlinna concept and its kinfolk with Diophantine approximation conception for graduate scholars and researchers.
This booklet with 9 chapters systematically describes Nevanlinna conception of meromorphic maps among algebraic kinds or complicated areas, increase from the classical thought of meromorphic features at the complicated airplane with complete proofs in Chap. 1 to the present country of research.
Chapter 2 offers the 1st major Theorem for coherent excellent sheaves in a really common shape. With the education of plurisubharmonic features, how the idea to be generalized in the next measurement is defined. In Chap. three the second one major Theorem for differentiably non-degenerate meromorphic maps through Griffiths and others is proved as a prototype of upper dimensional Nevanlinna theory.
Establishing this type of moment major Theorem for whole curves regularly advanced algebraic kinds is a wide-open challenge. In Chap. four, the Cartan-Nochka moment major Theorem within the linear projective case and the Logarithmic Bloch-Ochiai Theorem relating to common algebraic kinds are proved. Then the speculation of whole curves in semi-abelian forms, together with the second one major Theorem of Noguchi-Winkelmann-Yamanoi, is handled in complete information in Chap. 6. For that function Chap. five is dedicated to the thought of semi-abelian forms. the outcome ends up in a few purposes. With those effects, the Kobayashi hyperbolicity difficulties are mentioned in Chap. 7.
In the final chapters Diophantine approximation concept is handled from the perspective of upper dimensional Nevanlinna conception, and the Lang-Vojta conjecture is proven every so often. In Chap. eight the idea over functionality fields is mentioned. eventually, in Chap. nine, the theorems of Roth, Schmidt, Faltings, and Vojta over quantity fields are awarded and formulated in view of Nevanlinna idea with effects stimulated through these in Chaps. four, 6, and 7.