A couple of suggestions:

1. The word 'is' is rather pointless when you're using an =.
2. Using my implies that the variable is being initialized... and it doesn't make much sense to assign a varible, as it's being initialized, to another.

So, for instance, I might (assuming I were in love with Claudia as well) rewrite the first line as:

my $true_love = $Claudia;
# or perhaps
my $true_love = 'Claudia';
# or at least 
$Claudia = my $true_love;
[download]

Otherwise, I like it.

LAI, who has done way too much "real" poetry critique
:eof