Carex appalachia (Appalachian sedge) is a U.S. Northeast native sedge that enjoys dry shade but can tolerate full sun.  It is a cool season, deer resistant sedge that can be a successful and beautiful traditional lawn replacement. It has soft, graceful arching leaves. 

Photo Credit: https://upload.wikimedia.org/wikipedia/commons/thumb/3/37/Carex_appalachica_-_Brooklyn_Botanic_Garden_-_Brooklyn%2C_NY_-_DSC07918.JPG/1280px-Carex_appalachica_-_Brooklyn_Botanic_Garden_-_Brooklyn%2C_NY_-_DSC07918.JPG