Holdings: Nevanlinna theory in several complex variables and diophantine approximation

Nevanlinna theory in several complex variables and diophantine approximation:

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Bibliographic Details
Main Authors:	Noguchi, Junjiro 1948- (Author), Winkelmann, Jörg 1963- (Author)
Format:	Electronic eBook
Language:	English
Published:	Tokyo [u.a.] Springer 2014
Series:	Grundlehren der mathematischen Wissenschaften 350
Subjects:	Nevanlinna-Theorie Diophantische Approximation
Online Access:	DE-634 DE-861 DE-91 DE-384 DE-19 DE-703 DE-20 DE-739 Volltext Inhaltsverzeichnis Abstract
Physical Description:	1 Online-Ressource (XIV, 416 S.)
ISBN:	9784431545705 9784431545712
DOI:	10.1007/978-4-431-54571-2

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adam_text	NEVANLINNA THEORY IN SEVERAL COMPLEX VARIABLES AND DIOPHANTINE APPROXIMATION / NOGUCHI, JUNJIRO : 2014 TABLE OF CONTENTS / INHALTSVERZEICHNIS NEVANLINNA THEORY OF MEROMORPHIC FUNCTIONS FIRST MAIN THEOREM DIFFERENTIABLY NON-DEGENERATE MEROMORPHIC MAPS ENTIRE CURVES INTO ALGEBRAIC VARIETIES SEMI-ABELIAN VARIETIES ENTIRE CURVES INTO SEMI-ABELIAN VARIETIES KOBAYASHI HYPERBOLICITY NEVANLINNA THEORY OVER FUNCTION FIELDS DIOPHANTINE APPROXIMATION BIBLIOGRAPHY INDEX SYMBOLS DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT. NEVANLINNA THEORY IN SEVERAL COMPLEX VARIABLES AND DIOPHANTINE APPROXIMATION / NOGUCHI, JUNJIRO : 2014 ABSTRACT / INHALTSTEXT THE AIM OF THIS BOOK IS TO PROVIDE A COMPREHENSIVE ACCOUNT OF HIGHER DIMENSIONAL NEVANLINNA THEORY AND ITS RELATIONS WITH DIOPHANTINE APPROXIMATION THEORY FOR GRADUATE STUDENTS AND INTERESTED RESEARCHERS. THIS BOOK WITH NINE CHAPTERS SYSTEMATICALLY DESCRIBES NEVANLINNA THEORY OF MEROMORPHIC MAPS BETWEEN ALGEBRAIC VARIETIES OR COMPLEX SPACES, BUILDING UP FROM THE CLASSICAL THEORY OF MEROMORPHIC FUNCTIONS ON THE COMPLEX PLANE WITH FULL PROOFS IN CHAP. 1 TO THE CURRENT STATE OF RESEARCH. CHAPTER 2 PRESENTS THE FIRST MAIN THEOREM FOR COHERENT IDEAL SHEAVES IN A VERY GENERAL FORM. WITH THE PREPARATION OF PLURISUBHARMONIC FUNCTIONS, HOW THE THEORY TO BE GENERALIZED IN A HIGHER DIMENSION IS DESCRIBED. IN CHAP. 3 THE SECOND MAIN THEOREM FOR DIFFERENTIABLY NON-DEGENERATE MEROMORPHIC MAPS BY GRIFFITHS AND OTHERS IS PROVED AS A PROTOTYPE OF HIGHER DIMENSIONAL NEVANLINNA THEORY.ESTABLISHING SUCH A SECOND MAIN THEOREM FOR ENTIRE CURVES IN GENERAL COMPLEX ALGEBRAIC VARIETIES IS A WIDE-OPEN PROBLEM. IN CHAP. 4, THE CARTAN-NOCHKA SECOND MAIN THEOREM IN THE LINEAR PROJECTIVE CASE AND THE LOGARITHMIC BLOCH-OCHIAI THEOREM IN THE CASE OF GENERAL ALGEBRAIC VARIETIES ARE PROVED. THEN THE THEORY OF ENTIRE CURVES IN SEMI-ABELIAN VARIETIES, INCLUDING THE SECOND MAIN THEOREM OF NOGUCHI-WINKELMANN-YAMANOI, IS DEALT WITH IN FULL DETAILS IN CHAP. 6. FOR THAT PURPOSE CHAP. 5 IS DEVOTED TO THE NOTION OF SEMI-ABELIAN VARIETIES. THE RESULT LEADS TO A NUMBER OF APPLICATIONS. WITH THESE RESULTS, THE KOBAYASHI HYPERBOLICITY PROBLEMS ARE DISCUSSED IN CHAP. 7. IN THE LAST TWO CHAPTERS DIOPHANTINE APPROXIMATION THEORY IS DEALT WITH FROM THE VIEWPOINT OF HIGHER DIMENSIONAL NEVANLINNA THEORY, AND THE LANG-VOJTA CONJECTURE IS CONFIRMED IN SOME CASES. IN CHAP. 8 THE THEORY OVER FUNCTION FIELDS IS DISCUSSED. FINALLY, IN CHAP.9, THE THEOREMS OF ROTH, SCHMIDT, FALTINGS, AND VOJTA OVER NUMBER FIELDS ARE PRESENTED AND FORMULATED IN VIEW OF NEVANLINNA THEORY WITH RESULTS MOTIVATED BY THOSE IN CHAPS. 4, 6, AND 7 DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
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spelling	Noguchi, Junjiro 1948- Verfasser (DE-588)172286816 aut Nevanlinna theory in several complex variables and diophantine approximation Junjiro Noguchi ; Jörg Winkelmann Tokyo [u.a.] Springer 2014 1 Online-Ressource (XIV, 416 S.) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften 350 Nevanlinna-Theorie (DE-588)4239989-0 gnd rswk-swf Diophantische Approximation (DE-588)4135760-7 gnd rswk-swf Nevanlinna-Theorie (DE-588)4239989-0 s Diophantische Approximation (DE-588)4135760-7 s DE-604 Winkelmann, Jörg 1963- Verfasser (DE-588)133717615 aut Grundlehren der mathematischen Wissenschaften 350 (DE-604)BV049758308 350 https://doi.org/10.1007/978-4-431-54571-2 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027085906&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027085906&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract
spellingShingle	Noguchi, Junjiro 1948- Winkelmann, Jörg 1963- Nevanlinna theory in several complex variables and diophantine approximation Grundlehren der mathematischen Wissenschaften Nevanlinna-Theorie (DE-588)4239989-0 gnd Diophantische Approximation (DE-588)4135760-7 gnd
subject_GND	(DE-588)4239989-0 (DE-588)4135760-7
title	Nevanlinna theory in several complex variables and diophantine approximation
title_auth	Nevanlinna theory in several complex variables and diophantine approximation
title_exact_search	Nevanlinna theory in several complex variables and diophantine approximation
title_full	Nevanlinna theory in several complex variables and diophantine approximation Junjiro Noguchi ; Jörg Winkelmann
title_fullStr	Nevanlinna theory in several complex variables and diophantine approximation Junjiro Noguchi ; Jörg Winkelmann
title_full_unstemmed	Nevanlinna theory in several complex variables and diophantine approximation Junjiro Noguchi ; Jörg Winkelmann
title_short	Nevanlinna theory in several complex variables and diophantine approximation
title_sort	nevanlinna theory in several complex variables and diophantine approximation
topic	Nevanlinna-Theorie (DE-588)4239989-0 gnd Diophantische Approximation (DE-588)4135760-7 gnd
topic_facet	Nevanlinna-Theorie Diophantische Approximation
url	https://doi.org/10.1007/978-4-431-54571-2 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027085906&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027085906&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV049758308
work_keys_str_mv	AT noguchijunjiro nevanlinnatheoryinseveralcomplexvariablesanddiophantineapproximation AT winkelmannjorg nevanlinnatheoryinseveralcomplexvariablesanddiophantineapproximation

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