Do you have a DVI port? there is a small adapter that will change a DVI to an HDMI. Do you have any other ports on your monitor other than the HDMI that you could use instead so that you dont need an adapter?
DVI and HDMI carry identical signals, HDMI just uses a smaller connector and carries audio as well but using HDMI instead will not increase your picture quality at all. Either cable(assuming its a dual link DVI) will support up to 2560x1600 which is as high as they go these days.