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\usepackage{amsmath} | |
\usepackage{mathtools} | |
\usepackage{amsthm} | |
\usepackage{asymptote} | |
%\usepackage{mathtext} | |
\usepackage{graphicx} | |
%\usepackage{mathabx} | |
\usepackage{etoolbox} | |
\usepackage[cmtip,arrow]{xy} | |
\usepackage{pb-diagram,pb-xy} | |
%\usepackage{mathtools} | |
\usepackage{concrete} | |
%\usepackage{extarrows} | |
\usepackage{bm} | |
\usepackage{float} | |
\usepackage{hyperref} | |
\usepackage{csquotes} | |
\usepackage{tikz} | |
\usetikzlibrary{patterns} | |
\usepackage{tikz-cd} | |
\hypersetup{ | |
colorlinks, | |
citecolor=blue, | |
filecolor=black, | |
linkcolor=blue, | |
urlcolor=black | |
} | |
\usetikzlibrary{matrix} | |
\emergencystretch=5pt | |
\tolerance=600 | |
\makeatletter | |
\patchcmd{\@maketitle}{\LARGE}{\Large}{}{} | |
\makeatother | |
\renewcommand{\labelenumi}{(\theenumi)} | |
\renewcommand{\theenumii}{\roman{enumii}} | |
\renewcommand{\setminus}{-} | |
\numberwithin{equation}{section} | |
\newcommand{\mb}[1]{{\textbf {\textit#1}}}% bold italic letters | |
\newcommand{\field}[1]{\mathbb{#1}} | |
\def\C{\mathcal{C}} | |
\def\F{\mathcal{F}} | |
\def\vp{\varphi} | |
\def\GS{G_\Sigma} | |
\def\k{\mathbf{k}} | |
\newcommand{\CPinf}{\field{C}P^\infty} | |
\newcommand{\CP}{\field{C}P} | |
\newcommand{\R}{\field{R}} | |
\newcommand{\Q}{\field{Q}} | |
\newcommand{\Z}{\field{Z}} | |
\newcommand{\ZK}{\mathcal{Z_K}} | |
\newcommand{\ind}{\mathop{\rm ind}\nolimits} | |
%\newcommand{\sslash}{\mathbin{/\mkern-12mu/}} | |
\newcommand{\Zp}{\Z /p\Z} | |
\newcommand{\K}{\mathcal{K}} | |
\newcommand{\X}{\mathcal{X}} | |
\newcommand{\T}{\mathbb{T}} | |
\newcommand{\h}{h} | |
\newcommand{\E}{E} | |
\newcommand{\B}{B} | |
\newcommand{\mv}{mv} | |
\renewcommand{\Im}{\operatorname{Im}} | |
\newcommand{\D}{\mathbb{D}} | |
\newcommand{\Sirc}{\mathbb{S}} | |
\DeclareMathOperator*{\argmin}{arg\,min} | |
\DeclareMathOperator*{\argmax}{arg\,max} | |
\DeclareMathOperator*{\supp}{supp} | |
\DeclareMathOperator{\WDiv}{WDiv} | |
\DeclareMathOperator{\Div}{Div} | |
\DeclareMathOperator{\Pic}{Pic} | |
\DeclareMathOperator{\AffAut}{Aff} | |
\DeclareMathOperator{\PDiv}{PDiv} | |
\DeclareMathOperator{\Gr}{Gr} | |
\DeclareMathOperator{\Bl}{Bl} | |
\DeclareMathOperator{\Sym}{Sym} | |
\DeclareMathOperator{\cone}{cone} | |
\DeclareMathOperator{\Tame}{Tame} | |
\DeclareMathOperator{\Lie}{Lie} | |
\DeclareMathOperator{\Mat}{Mat} | |
\DeclareMathOperator{\Susp}{Susp} | |
\DeclareMathOperator{\ML}{ML} | |
\DeclareMathOperator{\rk}{rk} | |
\DeclareMathOperator{\codim}{codim} | |
\DeclareMathOperator{\FML}{FML} | |
\DeclareMathOperator{\Spec}{Spec} | |
\DeclareMathOperator{\LND}{LND} | |
\DeclareMathOperator{\HLND}{H-LND} | |
\DeclareMathOperator{\trdeg}{tr.deg} | |
\DeclareMathOperator{\Aut}{Aut} | |
\DeclareMathOperator{\NAut}{\widetilde{\Aut}} | |
\DeclareMathOperator{\End}{End} | |
\DeclareMathOperator{\SAut}{SAut} | |
\DeclareMathOperator{\Hom}{Hom} | |
\DeclareMathOperator{\Id}{Id} | |
\DeclareMathOperator{\Cl}{Cl} | |
\DeclareMathOperator{\Hopf}{Hf} | |
%\DeclareMathOperator{\div}{div} | |
\def\A{\mathcal{A}} | |
\newcommand{\XX}{\mathbb{X}} | |
\newcommand{\RR}{\mathbb{R}} | |
\newcommand{\mf}[1]{\mathfrak{#1}} | |
%\renewcommand{\K}{\mathbb{K}} | |
\renewcommand{\C}{\mathbb{C}} | |
\renewcommand{\Q}{\mathbb{Q}} | |
\newcommand{\Aff}{\mathbb{A}} | |
\newcommand{\PP}{\mathbb{P}} | |
\renewcommand{\Z}{\mathbb{Z}} | |
\newcommand{\sL}{\mathcal{L}} | |
\newcommand{\sX}{\mathcal{X}} | |
\newcommand{\Ga}{\mathbb{G}_a} | |
\newcommand{\mc}[1]{\mathcal{#1}} | |
\newcommand{\Gm}{\mathbb{G}_m} | |
\newcommand{\Ml}{\mathscr{S}} | |
\newcommand{\V}{\mathbb{V}} | |
\newcommand{\Dem}{\mathscr{R}} | |
\newcommand*{\ms}[1]{\mathscr{#1}} | |
\newcommand{\con}{\widetilde{\Aut}^0} | |
%\DeclareMathOperator{\deg}{deg} | |
\newcommand*{\HomG}[1]{\operatorname{Hom\;}_{\Z[#1]}} | |
\newcommand*{\XA}[1]{(\bm{X,A})^{#1}} | |
\newcommand*{\OrbG}[1]{\operatorname{Orb}_G(#1)} | |
\newcommand*{\FKGw}[1]{\widetilde{\mathcal{F}(#1,G)}} | |
\newcommand*{\MAC}[1]{\mathcal{Z}_{#1}} | |
\newcommand{\hol}{\ms{O}} | |
\newcommand{\HAut}{\Aut_{\operatorname{alg}}} | |
\renewcommand{\div}{\operatorname{div}} | |
\renewcommand{\ker}{\operatorname{Ker}} | |
\renewcommand{\it}{\itshape} | |
\renewcommand{\Re}{\operatorname{Re}} | |
\renewcommand{\ind}{\mathbb{1}} | |
\newcommand{\Grp}{C_\Psi} | |
\newcommand{\ra}{\rangle} | |
\newcommand{\la}{\langle} | |
\newcommand{\data}{\{\K;\mb{a}_1,\ldots,\mb{a}_m\}} | |
\newcommand{\datam}[1]{\{\K;\mb{a}_1,\ldots,\mb{a}_{#1}\}} | |
\newcommand\CE{\textit{C\!E}} | |
\newcommand{\VS}{V_\Sigma} | |
\newcommand{\CVS}{R(\VS)} | |
\newcommand{\ol}[1]{\overline{#1}} | |
\renewcommand{\O}{\ms{O}} | |
\def\a{\ol{\boldsymbol{a}}} | |
\def\Ker{\operatorname{Ker}} | |
\def\le{\leqslant} | |
\def\ge{\geqslant} | |
\def\Ka{\K_{\a}} | |
\def\ss{\subset} | |
\def\sse{\subseteq} | |
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