Greenov izrek o hiperravninah v kompleksnem projektivnem prostoru

magistrsko delo

Aleksander Simonič (Author), Franc Forstnerič (Mentor)

Abstract

Podlaga za vpeljavo Kobayashijeve hiperboličnosti za kompleksne mnogoterosti sta klasična izreka iz analize ene kompleksne spremenljivke: Schwarz-Pickova lema in mali Picardov izrek. V magistrskem delu dokažemo Greenovo projektivno posplošitev Picardovih izrekov: komplement unije $2n+1$ hiperravnin v splošnem položaju v ${\mathbb {CP}}^n$ je poln hiperboličen in hiperbolično vložen v ${\mathbb {CP}}^n$. To storimo z uporabo razširjenega Brodyjevega izreka za komplement hiperploskve v kompaktni kompleksni mnogoterosti in Borelove posplošitve malega Picardovega izreka, ki ga dokažemo s pomočjo prvega glavnega izreka in leme o odvodu logaritma teorije Nevanlinne za meromorfne funkcije.

Keywords

kompleksne mnogoterosti;Kobayashijeva hiperboličnost;hiperbolične vložitve;hiperravnine;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.09 - Master's Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[A. Simonič]
UDC:	515.17
COBISS:	18512985
Views:	746
Downloads:	206
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Green's theorem on hyperplanes in complex projective space
Secondary abstract:	The rationale behind introduction of the Kobayashi hyperbolicity for complex manifolds are two classical theorems of complex analysis in one variable, namely, the Schwarz-Pick lemma and the little Picard theorem. In the present master thesis Green's projective generalisation of Picard's theorems is proved: The complement of $2n+1$ hyperplanes in general position in ${\mathbb {CP}}^n$ is complete hyperbolic and hyperbolically imbedded in ${\mathbb {CP}}^n$. This is achieved by using the extended Brody theorem for complement of a hypersurface in a compact complex manifold and Borel's generalisation of the little Picard theorem, which proof uses the first main theorem and the logarithmic derivative lemma from Nevanlinna's theory of meromorphic functions.
Secondary keywords:	complex manifolds;Kobayashi hyperbolicity;hyperbolic imbeddings;hyperplanes;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 2. stopnja
Pages:	VIII, 46 str.
ID:	11008319