Hcfyk

documentclass[12pt,reqno,a4paper]amsart
usepackageextsizes
usepackageblindtext
textheight 9.3in textwidth 6.5in
calclayout
usepackageamsmath,amsthm,amsfonts,amssymb
usepackagehyperref
usepackagemathrsfs
usepackage[all]xy
usepackage[normalem]ulem
usepackagetikz-cd
usepackage[utf8]inputenc
usepackage[english]babel
begindocument
[begintikzcd
underlineV 
arrow[rrrrdd, bend left]
arrow[rrdddd, bend right] arrow[rrdd, dotted] & && & \
& & & & \
& & A arrow[dd] arrow[rr] & & B arrow[dd] \
& & & & \
& & C arrow[rr] & & D 
endtikzcd]
enddocument

above code is giving me following diagram

I used "phantom" technique to number part of commutative diagram. It did not work. I want to write

• (1) in the diagram enclosed by V,A,B


• (2) in the diagram enclosed by V,A,C


• (3) in the diagram enclosed by A,B,C,D

Can some one help me to see how to do this?

Is this what you mean?

You can add the labels to your diagram with no arrows:

[begintikzcd
underlineV 
arrow[rrrrdd, bend left]
arrow[rrdddd, bend right] arrow[rrdd, dotted] & && & \
& & (1) & & \
& (2) & A arrow[dd] arrow[rr] & & B arrow[dd] \
& & & (3) & \
& & C arrow[rr] & & D 
endtikzcd]

Just for fun: tikz-cd is based on TikZ so

documentclass[tikz]standalone
begindocument
begintikzpicture[y=0.8cm]
node (a) at (0,0) $A$;
node (b) at (2,0) $B$;
node (c) at (0,-2) $C$;
node (d) at (2,-2) $D$;
node (v) at (-2,2) $underlineV$;
draw[->] (a)--(b);
draw[->] (b)--(d);
draw[->] (a)--(c);
draw[->] (c)--(d);
draw[dotted,->] (v)--(a);
draw[->] (v) to[bend right] (c);
draw[->] (v) to[bend left] (b);
node at (1,-1) (3);
node at (0,1) (1);
node at (-1,0) (2);
endtikzpicture
enddocument

But I prefer this way (though the way I code it is not efficient)

documentclass[tikz]standalone
begindocument
begintikzpicture[y=0.8cm,>=stealth]
node (V) at (-2,2) phantom$underlineV$;
node (B) at (2,0) phantom$B$;
node (C) at (0,-2) phantom$C$;
fill[yellow!50] (0,0) rectangle (2,-2);
fill[green!20] (V) to[bend left] (B)--(2,0)--(0,0)--(V);
fill[blue!20] (V) to[bend right] (C)--(0,-2)--(0,0)--(V);
beginscope[every node/.style=fill=white,circle,draw]
 node (a) at (0,0) $A$;
 node (b) at (2,0) $B$;
 node (c) at (0,-2) $C$;
 node (d) at (2,-2) $D$;
 node (v) at (-2,2) $underlineV$;
endscope
draw[->] (a)--(b);
draw[->] (b)--(d);
draw[->] (a)--(c);
draw[->] (c)--(d);
draw[dashed,->] (v)--(a);
draw[->] (v) to[bend right] (c);
draw[->] (v) to[bend left] (b);
node at (1,-1) (3);
node at (0,1) (1);
node at (-1,0) (2);
endtikzpicture
enddocument

With phantom arrows:

documentclass[a4paper]article
usepackagetikz-cd

begindocument

[
begintikzcd[nodes in empty cells]
underlineV
 arrow[rrrrdd, bend left]
 arrow[rrdddd, bend right]
 arrow[rrdd, dotted]
 arrow[rrrrdd,phantom,"(1)" description]
 arrow[rrdddd,phantom,"(2)" description]
\
&&&&\
&& A arrow[dd] arrow[rr] & arrow[dd,phantom,"(3)" description] &
B arrow[dd] \
&&&&\
&& C arrow[rr] && D
endtikzcd
]

enddocument