I just have no clue how to draw these especially how to arrange the lines arbitrarily.

enter image description here

enter image description here

enter image description here

  • 1
    With TikZ it is certainly possible, other options include asymptote and pstricks. – user121799 Jun 5 at 22:11

I would use TikZ for that because this allows you to use loops for repeating elements and relative positioning.

 \draw (0,1) -- (0,4) node[above]{$\mathbb{P}^1$}
  (0,0) -- (4,4) node[above right]{$\tau_4$}
  (2,0) -- (2,4) node[above]{$U_q$};
 \foreach \Y [count=\Z starting from 0] in {0,1.5,2.5,3.5}
  {\draw (1,\Y) -- (4,\Y) \ifnum\Z=0
   (0.1,\Y) -- (-0.1,\Y) node[left]{\ifnum\Z=3
   \foreach \X in {1.5,2.5,3.5}
   {\draw[fill=white] (\X,\Y) circle[radius=1.5pt];}}

\draw (0,0) node[below]{$\widetilde{U}_0$} -- (0,3) 
 (-0.5,0.5) -- (3,0.5) node[pos=1.1]{$\widetilde{\tau}_2$}
 (-0.5,0.8) -- ++ (30:3) node[pos=1.1]{$\widetilde{\tau}_3$}
 (-0.2,2) -- ++ (70:3.6) node[pos=1.1]{$E_0$} coordinate[pos=0.8] (aux1)
 coordinate[pos=0.9] (aux2)
 ([xshift=-8mm]aux1) -- ++(-40:2.5) node[pos=1.1]{$\widetilde{\tau}_1$}
 ([xshift=-8mm]aux2) -- ++(-15:2.5) node[pos=1.1]{$\widetilde{\tau}_4$};

\begin{tikzpicture}[bullet/.style={circle,fill,inner sep=1pt}]
 \draw (0,0) -- (45:4) node[pos=0.2,bullet,label=above:$i$]{}

enter image description here

  • You're faster than the light. My compliments for the short time to realize the picture. – Sebastiano Jun 5 at 22:39
  • 1
    @Sebastiano We had this already: slow marmots get caught by the eagles. – user121799 Jun 5 at 22:40
  • @marmot Thank you. Somehow it take me longer to draw these pictures than understanding what a moduli space is... Another question how to adjust the labels of nodes a bit from the default positions? – Upc Jun 5 at 23:18
  • @Upc You can use e.g. node[pos=0.4,bullet,label={[outer sep=1em]above:$j$}]{} instead of node[pos=0.4,bullet,label=above:$j$]{} or globally say \tikzset{every label/.append style={outer sep=1em}}. There are many possibilities, including yshift and so on. (I feel that it is simpler than moduli spaces. ;-) – user121799 Jun 5 at 23:34

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