$a = 1, $b = 2, $c = 3; works, and that's exactly why my $a = 1, my $b = 2, my $c = 3; would work.

Although it looks odd, but from a Perl internal view, it is the same animal as the following (,which we see from day to day):

foreach $line (@lines) {
...
}
[download]

works, that's why

foreach my $line (@lines) {
...
}
[download]

Basically, Perl allows you to my variables on fly.

One more example for the same animal:

for (my $i = 1; $i < 10; $i ++) {
    print $i;
}
[download]