Does the DNA occupy multiple lines between the single header lines? (Ie. Is this a standard FASTA format file?)

If so, this might work for you:

#! perl -slw
use strict;
use Data::Dump qw[ pp ]; $Data::Dump::WIDTH = 80;

local $/ = '>';

my %sequences;

(undef) = scalar <DATA>; ## Discard first delimiter

while( my $record = <DATA> ) {
    my @lines = split "\n", $record;
    pop @lines if $lines[-1] eq '>';
    my $id = shift @lines;
    $sequences{ $id } = join'', @lines;
}

pp \%sequences;

__DATA__
>uc002yje.1 chr21:13973492-13974491
cccctgccccaccgcaccctggattactgcacgccaagaccctcacctga
acgcgccctacactctggcatgggggaacccggccccgcagagccctgga
CTCTGACATTGGAGGACTCCTCGGCTACGTCCTGGACTCCTGCACAAGAG
>uc002yje.2 chr21:13974492-13975432
cccctgccccaccgcaccctggattactgcacgccaagaccctcacctga
acgcgccctacactctggcatgggggaaaaaacccggccccgcagagccctgga
CTCTGACATTGGAGGACTCCTCGGCTACGTCCTGGACTCCTGCACAAGAG
>uc002yje.3 chr21:13975431-13976330
cccctgccccaccgcaccctggattactgcacgccaagaccctcacctga
acgcgccctacactctggcatgggggaacccggccccgcagagggccctgga
CTCTGACATTGGAGGACTCCTCGGCTACGTCCTGGACTCCTGCACAAGAG
[download]

Outputs

c:\test>fasta
{
  "uc002yje.1 chr21:13973492-13974491" => "cccctgccccaccgcaccctggattac
+tgcacgccaagaccctcacctgaacgcgccctacactctggcatgggggaacccggccccgcagagccc
+tggaCTCTGACATTGGAGGACTCCTCGGCTACGTCCTGGACTCCTGCACAAGAG",
  "uc002yje.2 chr21:13974492-13975432" => "cccctgccccaccgcaccctggattac
+tgcacgccaagaccctcacctgaacgcgccctacactctggcatgggggaaaaaacccggccccgcaga
+gccctggaCTCTGACATTGGAGGACTCCTCGGCTACGTCCTGGACTCCTGCACAAGAG",
  "uc002yje.3 chr21:13975431-13976330" => "cccctgccccaccgcaccctggattac
+tgcacgccaagaccctcacctgaacgcgccctacactctggcatgggggaacccggccccgcagagggc
+cctggaCTCTGACATTGGAGGACTCCTCGGCTACGTCCTGGACTCCTGCACAAGAG",
}
[download]