Three brothers have been charged with murder in the vicious Christmas Day bludgeoning of their sister’s husband, but authorities say the motive in the attack remains a mystery.

The victim, who was stomped, beaten and smashed with a shovel in the garage of his Jersey City home, was identified yesterday as Jeorge Alvendia, 44.

Elieser Paet, 44, beat Alvendia with a shovel while Paet’s brothers, Francis, 37, and Wilfred, 39, kicked and stomped him, according to the criminal complaints.

Alvendia’s wife, Noemy, 51, was not at the Roosevelt Avenue home when the killing took place, but arrived shortly afterward, Hudson County Prosecutor Edward DeFazio said.

The three men are being held at Hudson County jail in Kearny. Their bails were set at $500,000, cash only, on Monday by Judge Fred Theemling.

U.S. Immigration and Customs Enforcement was informed of the incident, given that all three men are residents of the Philippines, even though Wilfred Paet does have a visa to be in the United States.

DeFazio said the murder was the result of “an ongoing family dispute,” but he refused to provide further information on a possible motive.

Alvendia died of blunt force trauma to the head, and also suffered severe facial injuries and fractured ribs in the beating he was given at about 8 o’clock Christmas night, DeFazio said.

The Paet brothers were arrested and charged on Monday and all appeared in Central Judicial Processing court via video link from the jail yesterday.

“This is an extraordinary case in that you have three brothers simultaneously charged with a murder,” DeFazio said.

A man who identified himself as a friend of Noemy Alvendia answered the door at the home yesterday, but declined to comment on the incident.