Somerville Mayor Joseph Curtatone and the Somerville firefighters union, Local 76, are back at the negotiating table to hammer out a contract agreement, according to Ward 2 Alderman Maryann Heuston, chair of the Board of Aldermen's finance committee.

News that the parties have resumed contract negotiations comes a week after the two sides faced off in an escalating dispute about an arbitration decision that awards firefighters millions in retroactive pay.

Last week, the firefighters union won a court decision that upheld the arbitration decision, which awards firefighters at least $4.3 million in retroactive pay. (The mayor's office has said the decision's language is imprecise and it could cost the city even more than $4.3 million.)

Meanwhile, the mayor's office, arguing the city doesn't have money to afford the arbitration award, presented a plan that called for at least 30 layoffs and the closure of a neighborhood library.

The mayor's plan was before the Board of Aldermen's finance committee Wednesday night, but the committee held off on discussing the matter because the mayor's office and the firefighters have begun to negotiate again, according to Heuston.

Heuston said the mayor and Jay Colbert, president of Local 76, have "been engaged in conversation about potential terms for a new multi-year labor agreement between the city and its firefighters."

She added, "They both told me that they thought the conversations had been productive … the mayor has informed me that in light of these developments, he's deferring his presentation to the finance committee until such time as the city and its firefighters have conduced this latest round of discussions."

Heuston said, "Hopefully they are leading us in a very positive direction, positive for people who have concerns … about layoffs, about closings, but in a positive direction for the firefighters as well."

Ward 6 Aldermen Rebekah Gewirtz, who represents the neighborhood with its library on the chopping block, said of the development, "This is excellent news."

Brief background

The previous firefighters contract ended in 2007, and the city and Local 76 spent nearly three years trying to negotiate a new contract. However, they were unable to reach a contract agreement, so in 2010 the union brought the matter to the state's Joint Labor-Management Committee. In December, that committee issued the arbitration decision that awarded the city's firefighters, retroactively, a 2 percent raise every year since 2007, among other things.

The city challenged the arbitration decision in court, but last week the challenge was denied. In order to pay for the decision, the mayor's office put forth a plan that called for layoffs and the closure of the West Branch Library, outside Davis Square, an area of the city with a vocal and involved population.

A public hearing about the matter is scheduled for Jan. 30, at 6 p.m. at the Somerville High School auditorium.