The following command will create a local copy of the source code for you.

git clone https://github.com/anton-petrunin/gauss.git

Go into subfolder mppics/, run mpost pic, come back:

cd mppics/
mpost pic
mpost pic-hints
cd ..

Go into subfolder asy/, run asy for each .asy-file, come back:

cd asy
asy deformation.asy
...
cd ..

Run pdflatex, makeindex and biber:

pdflatex curves-and-surfaces.tex
makeindex curves-and-surfaces
biber curves-and-surfaces
pdflatex curves-and-surfaces.tex

To get arXiv.tar with all needed files do

tar -cvf arXiv.tar --files-from list-of-files.txt