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AlgGeo1.tex
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AlgGeo1.tex
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\input{AlgGeo1.tex.preamble}
\begin{document}
%% Title page
\title{Algebraische Geometrie I}
\author{Prof. Dr. Venjakob}
\maketitle
\tableofcontents{}
\newpage{}
\section*{Literatur}
\begin{itemize}
\item Görtz, Wedhorn. \emph{Algebraic Geometry I}
\item Hartshorne. \emph{Algebraic Geometry}
\item Shafarevich. \emph{Basic Algebraic Geometry 1 \& 2}
\item Grothendieck. \emph{Eléments de géometrie algébrique, EGA I-IV}
\end{itemize}
\paragraph{Kommutative Algebra}
\begin{itemize}
\item Brüske, Ischebeck, Vogel. \emph{Kommutative Algebra}
\item Kunz. \emph{Einführung in die kommutative Algebra und algebraische Geometrie}
\end{itemize}
\chapter{Prä-Varietäten}
\label{chap:prae-varietaeten}
\include{Chapter1/AlgGeo1-Chapter1-1_Einfuehrung}
\include{Chapter1/AlgGeo1-Chapter1-2_Die-Zariski-Topologie}
\include{Chapter1/AlgGeo1-Chapter1-3_Affine-algebraische-Mengen}
\include{Chapter1/AlgGeo1-Chapter1-4_Der-Hilbertsche-Nullstellensatz}
\include{Chapter1/AlgGeo1-Chapter1-5_Korrespondenz-zwischen-Radikalidealen}
\include{Chapter1/AlgGeo1-Chapter1-6_Irreduzible-topologische-Raeume}
\include{Chapter1/AlgGeo1-Chapter1-7_Irreduzible-algebraische-Mengen}
\include{Chapter1/AlgGeo1-Chapter1-8_Quasikompakte-und-noethersche-topologische-Raeume}
\include{Chapter1/AlgGeo1-Chapter1-9_Morphismen-von-affinen-algebraischen-Mengen}
\include{Chapter1/AlgGeo1-Chapter1-10_Unzulaenglichkeiten}
\include{Chapter1/AlgGeo1-Chapter1-11_Der-affine-Koordinatenring}
\include{Chapter1/AlgGeo1-Chapter1-12_Funktorielle-Eigenschaften-des-Koordinatenrings}
\include{Chapter1/AlgGeo1-Chapter1-13_Raeume-mit-Funktionen}
\include{Chapter1/AlgGeo1-Chapter1-14_Der-Raum-mit-Funktionen-zu-einer-affin-algebraischen-Menge}
\include{Chapter1/AlgGeo1-Chapter1-15_Funktorialitaet-der-Konstruktion}
\include{Chapter1/AlgGeo1-Chapter1-16_Definition-von-Praevarietaeten}
\include{Chapter1/AlgGeo1-Chapter1-17_Vergleich-mit-differenzierbaren-komplexen-Mannigfaltigkeiten}
\include{Chapter1/AlgGeo1-Chapter1-18_Topologische-Eigenschaften-von-Praevarietaeten}
\include{Chapter1/AlgGeo1-Chapter1-19_Offene-Untervarietaeten}
\include{Chapter1/AlgGeo1-Chapter1-20_Funktionenkoerper-einer-Praevarietaet}
\include{Chapter1/AlgGeo1-Chapter1-21_Abgeschlossene-Unterpraevarietaeten}
\include{Chapter1/AlgGeo1-Chapter1-22_Homogene-Polynome}
\include{Chapter1/AlgGeo1-Chapter1-23_Definition-des-projektiven-Raumes}
\include{Chapter1/AlgGeo1-Chapter1-24_Projektive-Varietaeten}
\include{Chapter1/AlgGeo1-Chapter1-25_Koordinatenwechsel-im-projektiven-Raum}
\include{Chapter1/AlgGeo1-Chapter1-26_Lineare-Unterraeume-des-projektiven-Raums}
\include{Chapter1/AlgGeo1-Chapter1-27_Kegel}
\include{Chapter1/AlgGeo1-Chapter1-28_Quadriken}
\chapter{Das Ringspektrum}
\label{chap:das-ringspektrum}
\include{Chapter2/AlgGeo1-Chapter2-1_Definition-von-Spec-A}
\include{Chapter2/AlgGeo1-Chapter2-2_Topologische-Eigenschaften-von-Spec-A}
\include{Chapter2/AlgGeo1-Chapter2-3_Der-Funktor-A-Spec-A}
\include{Chapter2/AlgGeo1-Chapter2-4_Beispiele}
\include{Chapter2/AlgGeo1-Chapter2-5_Garben}
\include{Chapter2/AlgGeo1-Chapter2-6_Halme-von-Garben}
\include{Chapter2/AlgGeo1-Chapter2-7_Die-zu-einer-Praegarbe-assoziierte-Garbe}
\include{Chapter2/AlgGeo1-Chapter2-8_Direktes-und-inverses-Bild-von-Garben}
\include{Chapter2/AlgGeo1-Chapter2-9_Lokal-geringte-Raeume}
\include{Chapter2/AlgGeo1-Chapter2-10_Die-Strukturgarbe-auf-Spec-A}
\include{Chapter2/AlgGeo1-Chapter2-11_Der-Funktor-A-Spec-A}
\include{Chapter2/AlgGeo1-Chapter2-12_Beispiele}
\chapter{Schemata}
\label{chap:schemata}
\include{Chapter3/AlgGeo1-Chapter3-1_Schemata}
\include{Chapter3/AlgGeo1-Chapter3-2_Offene-Unterschemata}
\include{Chapter3/AlgGeo1-Chapter3-3_Morphismen-in-affinen-Schemata-hinein}
\include{Chapter3/AlgGeo1-Chapter3-4_Morphismen-der-Form-Spec-K-X}
\include{Chapter3/AlgGeo1-Chapter3-5_Verkleben-von-Schemata-und-disjunkte-Vereinigung}
\include{Chapter3/AlgGeo1-Chapter3-6_Der-projektive-Raum-als-Schema}
\include{Chapter3/AlgGeo1-Chapter3-7_Nullstellenmenge-im-projektiven-Raum}
\include{Chapter3/AlgGeo1-Chapter3-8_Topologische-Eigenschaften}
\include{Chapter3/AlgGeo1-Chapter3-9_Noethersche-Schemata}
\include{Chapter3/AlgGeo1-Chapter3-10_Generische-Punkte}
\include{Chapter3/AlgGeo1-Chapter3-11_Reduzierte-und-ganze-Schemata}
\include{Chapter3/AlgGeo1-Chapter3-12_Schemata-von-endlichem-Typ-ueber-k}
\include{Chapter3/AlgGeo1-Chapter3-13_Sehr-dichte-Teilmengen}
\include{Chapter3/AlgGeo1-Chapter3-14_Praevarietaeten-als-Schemata}
\include{Chapter3/AlgGeo1-Chapter3-15_Offene-und-abgeschlossene-Einbettung}
\include{Chapter3/AlgGeo1-Chapter3-16_Unterschemata-und-Einbettung}
\include{Chapter3/AlgGeo1-Chapter3-17_Projektive-und-quasiprojektive-Schemata-ueber-einen-Koerper}
\include{Chapter3/AlgGeo1-Chapter3-18_Reduzierte-Unterschemata}
\chapter{Faserprodukte}
\label{chap:faserprodukte}
\include{Chapter4/AlgGeo1-Chapter4-1_Der-Punkte-Funktor}
\include{Chapter4/AlgGeo1-Chapter4-2_Yoneda-Lemma}
\include{Chapter4/AlgGeo1-Chapter4-3_Faserprodukte-in-beliebigen-Kategorien}
\include{Chapter4/AlgGeo1-Chapter4-4_Faserprodukte-von-Schemata}
\include{Chapter4/AlgGeo1-Chapter4-5_Beispiele}
\include{Chapter4/AlgGeo1-Chapter4-6_Basiswechsel}
\include{Chapter4/AlgGeo1-Chapter4-7_Fasern-von-Morphismen}
\include{Chapter4/AlgGeo1-Chapter4-8_Eigenschaften-von-Schemata-Morphismen}
\include{Chapter4/AlgGeo1-Chapter4-9_Urbilder-und-Schema-theoretische-Schnitte-von-Unterschemata}
\include{Chapter4/AlgGeo1-Chapter4-10_Affine-und-projektive-Raeume-ueber-beliebige-Basen}
\include{Chapter4/AlgGeo1-Chapter4-11_Diagonal-Graph-und-Kern-in-beliebigen-Kategorien}
\include{Chapter4/AlgGeo1-Chapter4-12_Diagonal-fuer-Schemata}
\include{Chapter4/AlgGeo1-Chapter4-13_Separierte-Morphismen}
\include{Chapter4/AlgGeo1-Chapter4-14_Eigentliche-Morphismen}
\chapter{Dimensionen}
\label{chap:dimensionen}
\include{Chapter5/AlgGeo1-Chapter5-1_Allgemeine-Schemata}
\newpage{}
\printindex{}
\end{document}