The long-awaited renovation of Father Demo Square on Sixth Ave. at Bleecker St. recently got underway, as a construction fence was put up around the triangular plaza about two weeks ago. Depending on the severity of the winter weather, the renovation is expected to last up to nine months. Budgeted at $1.3 million, the project will include installation of a new fountain, as well as a 3-foot-high fence similar to those ringing the nearby Sixth Ave. small “vest-pocket” parks. The uneven plaza will be leveled, the irrigation system redone, trees replanted and new lights embedded in the ground. Although until now the park has been used throughout the night, it’s expected there will be a curfew once it reopens. David Gruber, president of the Carmine Street Block Association, said the community favors a 1 a.m. or 2 a.m. curfew and that the low fence will help police convince people that the park is closed. “The community wanted to have it secured overnight and safe and quiet,” Gruber said. “A lot of people live around there. We need to have some crowd control.” It’s not clear, however, if any pigeon-control plan is in the works for the plaza, which is usually festooned with pigeon droppings.