\NeedsTeXFormat{LaTeX2e} \ProvidesPackage{FPSACmoduli} % all styling here %% Editing comments \def\seeEditComments{1} % 1 to see edit comments, 0 to hide them %% Load Packages \RequirePackage{amsmath, amssymb, amsthm} \RequirePackage{hyperref} % for drawing and commutative diagrams \RequirePackage{tikz, tikz-cd} \RequirePackage{mathtools,blkarray} \RequirePackage{algorithmicx,algpseudocode} \RequirePackage{stmaryrd} \RequirePackage{graphicx,color,xcolor,soul} \RequirePackage{float,multirow} \RequirePackage{caption,subcaption} \RequirePackage{algorithm} \RequirePackage{indentfirst, enumitem} \RequirePackage{blkarray} \RequirePackage{eqnarray} \RequirePackage{listings} \RequirePackage{diagbox} \RequirePackage{comment} %% END of packages %% Theorem-like environments % other types have the same numbering as "Theorem" \theoremstyle{plain} \newtheorem{thm}{Theorem}[section] \newtheorem{lem}[thm]{Lemma} \newtheorem{cor}[thm]{Corollary} \newtheorem{prop}[thm]{Proposition} \newtheorem{conj}[thm]{Conjecture} \theoremstyle{definition} \newtheorem{defn}[thm]{Definition} \newtheorem{exmp}[thm]{Example} \theoremstyle{definition} \newtheorem{rmk}[thm]{Remark} % Each type has independent numbering % \theoremstyle{plain} % \newtheorem{thm}{Theorem}[section] % \newtheorem{lem}{Lemma}[section] % \newtheorem{cor}{Corollary}[section] % \newtheorem{prop}{Proposition}[section] % \newtheorem{conj}{Conjecture} % \theoremstyle{definition} % \newtheorem{defn}{Definition}[section] % \newtheorem{exmp}{Example}[section] %% mathbb \newcommand{\Z}{\mathbb{Z}} \newcommand{\R}{\mathbb{R}} \newcommand{\Zge}{\Z_{\ge 0}} % non-negative integers \newcommand{\Zgt}{\Z_{> 0}} % positive integers \newcommand{\C}{\mathbb{C}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\van}{\mathbb{V}} % vanishing set - zero locus \newcommand{\Pj}{\mathbb{P}} % projective \newcommand{\A}{\mathbb{A}} % affine % mathfrak \newcommand{\mfa}{\mathfrak{a}} \newcommand{\mfb}{\mathfrak{b}} \newcommand{\mfc}{\mathfrak{c}} \newcommand{\mfd}{\mathfrak{d}} \newcommand{\mfe}{\mathfrak{e}} \newcommand{\mff}{\mathfrak{f}} \newcommand{\mfg}{\mathfrak{g}} \newcommand{\mfh}{\mathfrak{h}} \newcommand{\mfi}{\mathfrak{i}} \newcommand{\mfj}{\mathfrak{j}} \newcommand{\mfk}{\mathfrak{k}} \newcommand{\mfl}{\mathfrak{l}} \newcommand{\mfm}{\mathfrak{m}} \newcommand{\mfn}{\mathfrak{n}} \newcommand{\mfo}{\mathfrak{o}} \newcommand{\mfp}{\mathfrak{p}} \newcommand{\mfq}{\mathfrak{q}} \newcommand{\mfr}{\mathfrak{r}} \newcommand{\mfs}{\mathfrak{s}} \newcommand{\mft}{\mathfrak{t}} \newcommand{\mfu}{\mathfrak{u}} \newcommand{\mfv}{\mathfrak{v}} \newcommand{\mfw}{\mathfrak{w}} \newcommand{\mfx}{\mathfrak{x}} \newcommand{\mfy}{\mathfrak{y}} \newcommand{\mfz}{\mathfrak{z}} \newcommand{\mfA}{\mathfrak{A}} \newcommand{\mfB}{\mathfrak{B}} \newcommand{\mfC}{\mathfrak{C}} \newcommand{\mfD}{\mathfrak{D}} \newcommand{\mfE}{\mathfrak{E}} \newcommand{\mfF}{\mathfrak{F}} \newcommand{\mfG}{\mathfrak{G}} \newcommand{\mfH}{\mathfrak{H}} \newcommand{\mfI}{\mathfrak{I}} \newcommand{\mfJ}{\mathfrak{J}} \newcommand{\mfK}{\mathfrak{K}} \newcommand{\mfL}{\mathfrak{L}} \newcommand{\mfM}{\mathfrak{M}} \newcommand{\mfN}{\mathfrak{N}} \newcommand{\mfO}{\mathfrak{O}} \newcommand{\mfP}{\mathfrak{P}} \newcommand{\mfQ}{\mathfrak{Q}} \newcommand{\mfR}{\mathfrak{R}} \newcommand{\mfS}{\mathfrak{S}} \newcommand{\mfT}{\mathfrak{T}} \newcommand{\mfU}{\mathfrak{U}} \newcommand{\mfV}{\mathfrak{V}} \newcommand{\mfW}{\mathfrak{W}} \newcommand{\mfX}{\mathfrak{X}} \newcommand{\mfY}{\mathfrak{Y}} \newcommand{\mfZ}{\mathfrak{Z}} % mathcal \newcommand{\mcA}{\mathcal{A}} \newcommand{\mcB}{\mathcal{B}} \newcommand{\mcC}{\mathcal{C}} \newcommand{\mcD}{\mathcal{D}} \newcommand{\mcE}{\mathcal{E}} \newcommand{\mcF}{\mathcal{F}} \newcommand{\mcG}{\mathcal{G}} \newcommand{\mcH}{\mathcal{H}} \newcommand{\mcI}{\mathcal{I}} \newcommand{\mcJ}{\mathcal{J}} \newcommand{\mcK}{\mathcal{K}} \newcommand{\mcL}{\mathcal{L}} \newcommand{\mcM}{\mathcal{M}} \newcommand{\mcN}{\mathcal{N}} \newcommand{\mcO}{\mathcal{O}} \newcommand{\mcP}{\mathcal{P}} \newcommand{\mcQ}{\mathcal{Q}} \newcommand{\mcR}{\mathcal{R}} \newcommand{\mcS}{\mathcal{S}} \newcommand{\mcT}{\mathcal{T}} \newcommand{\mcU}{\mathcal{U}} \newcommand{\mcV}{\mathcal{V}} \newcommand{\mcW}{\mathcal{W}} \newcommand{\mcX}{\mathcal{X}} \newcommand{\mcY}{\mathcal{Y}} \newcommand{\mcZ}{\mathcal{Z}} %% math operators \DeclareMathOperator{\id}{id} \DeclareMathOperator{\Spec}{Spec} \DeclareMathOperator{\Sym}{Sym} \DeclareMathOperator{\Br}{Br} \DeclareMathOperator{\val}{val} \DeclareMathOperator{\Aut}{Aut} \DeclareMathOperator{\codim}{codim} \DeclareMathOperator{\Bl}{Bl} \DeclareMathOperator{\Mar}{Mar} \DeclareMathOperator{\GL}{GL} \DeclareMathOperator{\aff}{aff} \DeclareMathOperator{\Int}{int} \DeclareMathOperator{\rank}{rank} \DeclareMathOperator{\Conf}{Conf} % ordered (planar) rooted trees with every internal vertex having >=2 children \DeclareMathOperator{\Rtree}{Rtree} % (full) binary trees subset of stable rooted trees % \DeclareMathOperator{\BinRtree}{BinRtree} % stable rooted trees \DeclareMathOperator{\StRtree}{StRtree} % refined stable rooted trees \DeclareMathOperator{\RStRtree}{RStRtree} % \DeclareMathOperator{\Rleaf}{Rleaf} % \DeclareMathOperator{\Lleaf}{Lleaf} % \DeclareMathOperator{\attach}{attach} %% add "^*" for recursive flips % flip nonrecursively at a vertex including root \DeclareMathOperator{\flip}{flip} % flip at a root \DeclareMathOperator{\rflip}{rflip} % flip at any vertex but the root \DeclareMathOperator{\nrflip}{\overline{rflip}} %%% general math related mcros % embedding into \newcommand{\into}{\hookrightarrow} % surjects onto \newcommand{\onto}{\twoheadrightarrow} % white circle \newcommand{\whitecircle}{\tikz\draw[black,fill=white] (0,0) circle (.5ex);} % ceiling and floor commands \newcommand{\ceil}[1]{\lceil {#1}\rceil} \newcommand{\floor}[1]{\lfloor {#1}\rfloor} % raise to the power of -1 \newcommand{\inv}[1]{{#1}^{-1}} % set subtraction \newcommand{\ssub}{\setminus} % \subto{x}{n} yields x_1...x_n \newcommand{\subto}[2]{{#1}_1\hdots{#1}_{#2}} % \subtoComma{x}{n} yields x_1,...,x_n \newcommand{\subtoComma}[2]{{#1}_1,\hdots,{#1}_{#2}} % zero vector (arrow on top) \newcommand{\veczero}{\vec{0}} % double cover notation % \newcommand{\DC}[1]{{#1}^{2:1}} \newcommand{\DC}[1]{\widetilde{#1}} % generator or generated by \newcommand{\gen}[1]{\langle {#1} \rangle} % WLOG \newcommand{\WLOG}{Without loss of generality} %SES \newcommand{\SES}{short exact sequence\ } \newcommand{\littlecell}{\tau_{\text{little}}} \newcommand{\bigcell}{\tau_{\text{big}}} %%% Utility for M_0,n-bar and Hassett space % typeset M_0,n given the n parameter \newcommand{\moduli}[1]{M_{0,{#1}}} \newcommand{\moduliDC}[1]{\DC{M_{0,#1}}} \newcommand{\DMumford}[1]{\overline{\moduli{#1}}} %deprecate \newcommand{\DMumfordDC}[1]{\overline{\moduliDC{#1}}} % symmetric hassett space with weight \mcA(a), a: parameter \newcommand{\hassett}[1]{\DMumford{\mcA({#1})}} \newcommand{\hassettDC}[1]{\moduliDC{\mcA({#1})}} %% Draw a marked point on a tree of P^1's % Arguments: % #1 The tikz node corresponding to the component (P^1 bubble) containing this marked point % #2 Angle in degrees (from rightmost CCW) to place the marked point % #3 Label on the outside % #4 label on the inside \newcommand{\markedpoint}[4]{ \node[black, % with the color defined by the macro draw, %thick, % draw the outline fill, % fill it inner sep = 0pt, % not too big minimum size=1.5mm, % set the size circle, % circular shape label={ {#2} : {#4} }, % add the number on the inside label = {{#2+180} : {#3} } % add the number on the outside ] at ({#1}.{#2}) % position it on the edge of the main circle {} } %%% Macros for some rooted tree drawings %% Tree with 2 leaves % #1 - label of the left leaf % #2 - right leaf \newcommand{\trivialTree}[2]{ %leaves \node [circle, draw, fill, inner sep =1pt, label = { 90: {#1}}] (node_1_-1) at (1,-2) {}; \node [circle, draw, fill, inner sep =1pt, label = { 90: {#2}}] (node_5'0_-2) at (5.0,-2) {}; %root \node [circle, draw, fill, inner sep =1pt, label = { 90: }] (node_3'0_-3) at (3.0,-4) {}; %edges \draw[] (node_3'0_-3) -- (node_1_-1); \draw[] (node_3'0_-3) -- (node_5'0_-2); } \newcommand{\deprecate}[1]{\par\ {\color{gray}{\hrulefill\\ \underline{\textbf{Deprecated (will be removed soon): }\\} {#1} }~\\ } \hrulefill } % EXTRA logic \if\seeEditComments1 \newcommand{\plan}[1]{\par\textcolor{blue}{\underline{\textbf{Plan: }} {#1}}~\\} \newcommand{\JL}[1]{\par\ {\color{red}{JL: {#1}}}} \newcommand{\HL}[1]{\par\ {\color{blue}{\underline{\textbf{HL: }} {#1}}}~\\} \fi \if\seeEditComments0 \newcommand{\plan}[1]{} \newcommand{\JL}[1]{} \newcommand{\HL}[1]{} \fi