Poana grass, also known as Poa annua, is a type of bluegrass and is considered by many to be an invasive species of weed. Once poana has established itself, if can be very difficult to eradicate. There are no herbicides specifically formulated to kill only poana grass, so chemical means to deal with this weed involve the risk of killing other plants as well. And while chemical herbicides can do the job, there is another way of dealing with poana that is completely organic--smothering it.
Mow the poana grass to approximately 1/2 inch.
Spread 10 sheets of newspaper over the area you wish to kill and dampen the newspaper with a mist of water from your garden hose.
Cover the newspaper with 1 inch of mulch and spray lightly with the garden hose one last time. The newspaper and mulch will effectively block all sunlight from the poana grass, killing it.
Continue dampening the newspaper/mulch lightly for four weeks. The dampness will help to weigh the newspaper down and keep it in place and also aids in the decomposition of the newspaper. After four weeks of darkness, the area is now poana grass-free and ready for whatever use you wish to put the area to.