\documentclass[12pt]{article}\usepackage[all]{xy}
\usepackage{german,a4,amsmath,amssymb,amsfonts,amscd,mathrsfs}
\addtolength{\topmargin}{-40pt}
\addtolength{\textheight}{84pt}
\setlength{\textwidth}{16cm}
\parindent0mm
%\pagestyle{empty}
%\evensidemargin-0.5cm
%\oddsidemargin1.4cm

\sloppy

\newtheorem{theorem}{Satz}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Korollar}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{satzdef}[theorem]{Satz/Definition}
\newtheorem{Def}[theorem]{Definition}
\newcommand{\Alb}{{\rm Alb}}
\newcommand{\alb}{{\rm alb}}
\newcommand{\dee}{\partial}
\newcommand{\rk}{{\rm rk}}
\newcommand{\Hom}{{\rm Hom}}
\newcommand{\GL}{{\rm GL}}
\newcommand{\Grass}{{\rm Grass}}
\newcommand{\length}{{\rm length}}
\newcommand{\Pic}{{\rm Pic}}
\newcommand{\Jac}{{\rm Jac}}
\newcommand{\Ext}{{\rm Ext}}
\newcommand{\Tor}{{\rm Tor}}
\newcommand{\Spec}{{\rm Spec}}
\newcommand{\Sing}{{\rm Sing}}
\newcommand{\Quot}{{\rm Quot}}
\newcommand{\Hilb}{{\rm Hilb}}
\newcommand{\coker}{{\rm coker}}
\newcommand{\SL}{{\rm SL}}
\newcommand{\Proj}{{\rm Proj}}
\newcommand{\HNP}{{\rm HNP}}
\newcommand{\Hol}{{\rm Hol}}
\newcommand{\Orth}{{\rm O}}
\newcommand{\U}{{\rm U}}
\newcommand{\SU}{{\rm SU}}
\newcommand{\NS}{{\rm NS}}
\newcommand{\id}{{\rm id}}
\newcommand{\im}{{\rm im}}
\newcommand{\gr}{{\rm gr}}
\newcommand{\sgn}{{\rm sgn}}
\newcommand{\ext}{{\rm ext}}
\newcommand{\ch}{{\rm ch}}
\newcommand{\Td}{{\rm Td}}
\newcommand{\ord}{{\rm ord}}
\newcommand{\triv}{{\rm triv}}
\newcommand{\tr}{{\rm tr}}
\newcommand{\supp}{{\rm supp}}
\newcommand{\ggT}{{\rm ggT}}
\newcommand{\kgV}{{\rm kgV}}

\newcommand{\Bcal}{{\cal B}}
\newcommand{\Ccal}{{\cal C}}
\newcommand{\Ecal}{{\cal E}}
\newcommand{\Fcal}{{\cal F}}
\newcommand{\Gcal}{{\cal G}}
\newcommand{\Hcal}{{\cal H}}
\newcommand{\Jcal}{{\cal J}}
\newcommand{\Lcal}{{\cal L}}
\newcommand{\Mcal}{{\cal M}}
\newcommand{\Ocal}{{\cal O}}
\newcommand{\Pcal}{{\cal P}}
\newcommand{\Rcal}{{\cal R}}
\newcommand{\Zcal}{{\cal Z}}

\newcommand{\ccc}{\underline{c}}

\newcommand{\Aold}{{\bf A}}
\newcommand{\Bold}{{\bf B}}
\newcommand{\Mold}{{\bf M}}
\newcommand{\Xold}{{\bf X}}
\newcommand{\Yold}{{\bf Y}}

\newcommand{\cdop}{{\mathbb C}}
\newcommand{\fdop}{{\mathbb F}}
\newcommand{\hdop}{{\mathbb H}}
\newcommand{\qdop}{{\mathbb Q}}
\newcommand{\ndop}{{\mathbb N}}
\newcommand{\rdop}{{\mathbb R}}
\newcommand{\pdop}{{\mathbb P}}
\newcommand{\zdop}{{\mathbb Z}}

\newcommand{\shom}{\underline{\Hom}}
\newcommand{\send}{{{\cal E} nd}}
\newcommand{\hhom}{I \!\! \Hom}
\newcommand{\hext}{I \!\! Ext}

\newcommand{\dual}{^\lor}
\newcommand{\ddual}{^{\lor \lor}}
\newcommand{\elem}{\epsilon}
\newcommand{\rar}{\rightarrow}
\newcommand{\Rar}{\Rightarrow}
\newcommand{\rarpa}[1]{\stackrel{#1}{\rightarrow}}
\newcommand{\dar}{\downarrow}
\newcommand{\Lrar}{\Leftrightarrow}
\newcommand{\lar}{\leftarrow}
\newcommand{\larpa}[1]{\stackrel{#1}{\leftarrow}}

\newcommand{\remark}{{\bf Bemerkung: }}
\newcommand{\example}{{\bf Beispiel: }}
\newcommand{\proof}{{\bf Beweis: }}
\newcommand{\definition}{{\bf Definition: }}
\newcommand{\case}[1]{{\bf Fall #1: }}
\newcommand{\step}[1]{{\bf Schritt #1: \hspace{0.2em} }}
\newcommand{\qed}{{ \hfill $\Box$}}
\newcommand{\tiptop}{{\vspace{1.2em} }}
\newcommand{\tip}{{\vspace{0.5em} }}
\newcommand{\sz}{"s}
\newcommand{\sZ}{"s \hspace{0.1em}}


