This weed is so terribly invasive, it takes over the lawn grass which I think is broadleaf carpetgrass (which we call savannah grass here in the West Indies). It seems to occur in profusion in areas of the garden where it's wetter, and has an interlocking system of roots which makes it really difficult to kill. It looks like nutsedge, I find, but I really don't know. Is it? How to I get rid of it but save the grass in between?
Looks like a grass rather than a sedge, there are thousands of kinds of grasses. Can't really get too far on identification without flowerheads although someone from your area may know a common one there that looks similar in leaf.
