000 04287nam a22005175i 4500
001 978-4-431-54571-2
003 DE-He213
005 20140220082525.0
007 cr nn 008mamaa
008 131209s2014 ja | s |||| 0|eng d
020 _a9784431545712
_9978-4-431-54571-2
024 7 _a10.1007/978-4-431-54571-2
_2doi
050 4 _aQA331-355
072 7 _aPBKD
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.9
_223
100 1 _aNoguchi, Junjiro.
_eauthor.
245 1 0 _aNevanlinna Theory in Several Complex Variables and Diophantine Approximation
_h[electronic resource] /
_cby Junjiro Noguchi, Jörg Winkelmann.
264 1 _aTokyo :
_bSpringer Japan :
_bImprint: Springer,
_c2014.
300 _aXIV, 416 p. 6 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v350
505 0 _aNevanlinna 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.
520 _aThe 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.
650 0 _aMathematics.
650 0 _aGeometry, algebraic.
650 0 _aFunctions of complex variables.
650 0 _aDifferential equations, partial.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aFunctions of a Complex Variable.
650 2 4 _aSeveral Complex Variables and Analytic Spaces.
650 2 4 _aAlgebraic Geometry.
650 2 4 _aNumber Theory.
700 1 _aWinkelmann, Jörg.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9784431545705
830 0 _aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
_x0072-7830 ;
_v350
856 4 0 _uhttp://dx.doi.org/10.1007/978-4-431-54571-2
912 _aZDB-2-SMA
999 _c93713
_d93713