In Perl, what is omitted precisely when you declare variables with omitting default values?

declare.pl

use strict;
use warnings;
use feature qw(say);

say "## scalars ##";    # スカラは通る

say "---- omitted ----", my $empty;    # 省略
if ( defined $empty ) {
    die "it's defined! You are Liar!";
} else {
    say "is's not defined";
}

say "---- with () ----", $empty = ();    # ()で宣言
if ( defined $empty ) {
    die "it's defined! You are Liar!";
} else {
    say "is's not defined";
}

say "---- with undef ----", $empty = undef;    # undefで宣言
if ( defined $empty ) {
    die "it's defined! You are Liar!";
} else {
    say "is's not defined";
}

say "## Arrays ##";                            # 配列は

say "---- omitted ----", my @empties;           # 省略
if (@empties) {
    die "it's defined! You are Liar!";
} else {
    say "is's not defined";
}

say "---- with () ----", @empties = ();        # ()で宣言
if (@empties) {
    die "it's defined! You are Liar!";
} else {
    say "is's not defined";
}

say "---- with undef ----", @empties = undef;    # undefで宣言すると

# @empties = (undef);                            # の省略と見做されるので
if (@empties) {
    die "it's defined! You are Liar!";           # ここで止まる
} else {
    say "is's not defined";
}

say "Tests passed";
exit;