The incident, which appeared to be a domestic dispute, was reported in the area of Bergen and Virginia avenues around 7 a.m.
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The victim was shot several times on the third floor of the Toy Factory apartments.
She was identified by the superintendent of Jersey City Public Schools as a Temara King:
"Our hearts are broken at the sudden loss of Temara King. She was an outstanding teacher and educated member of our district. She will be missed and our prayers go to her family and friends as they cope with the tragedy."
According to the district website, King was a third-grade teacher.
The gunman, who apparently lives in the complex, was apprehended later Tuesday afternoon, authorities said.
The victim's daughter called police right after the shooting and told them who was responsible for the crime.
A neighbor saw the gunman just moments before the shooting and said he appeared to be upset and distracted.
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The case is being investigated by both the Jersey City Police Department and the Hudson County Prosecutor's Office.
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