  We studied the trance distance, the Hellinger distance, and the Bures
distance geometric quantum discords (GQDs) for a two-spin Heisenberg {\it XX}
chain with the Dzyaloshinsky-Moriya (DM) interaction and the external magnetic
fields. We found that considerable enhancement of the GQDs can be achieved by
introducing the DM interaction, and their maxima were obtained in the limiting
case $D\rightarrow \infty$. The external magnetic fields and the increase of
the temperature can also enhance the GQDs to some extent for certain special
cases.
