A man in his late 20s - who is believed to be known to Ms Fonseca - was arrested this morning
Ms Fonseca was originally from South America but had been living in Cork for several years.
Detectives are treating her death as suspicious amid indications she met a violent death.
Gardaí investigating her death have arrested a man.
The man in his late 20s - who is believed to be known to Ms Fonseca - was arrested this morning and is currently detained under Section 4 of the Criminal Justice Act, 1984 in Bridewell Garda Station, Cork.
Ms Fonseca was discovered in an apartment on Liberty Street, just off North Main Street, in the early hours of Sunday morning.
Gardaí and emergency services were alerted to the incident at approximately 6.30am and she was found unresponsive in an apartment.
The property is just off Cork city centre and only a short distance from Cork Courthouse on Washington Street and the Bridewell garda station.
Gardaí and paramedics attended the scene but she was pronounced dead a short time later.
The scene was immediately sealed off to allow for a full forensic and technical examination.
Gardaí will begin an examination of CCTV security camera footage from business premises in the area to determine all movements to and from the premises involved over the past 24 hours.
Ms Fonseca’s body will be transferred to Cork University Hospital pending a full post mortem examination by Assistant State Pathologist, Dr Margot Bolster.
Garda sources stressed that the results of the post mortem examination will now determine the nature of their investigation.
However, the death is being treated as suspicious.
Gardaí have also commenced door-to-door inquiries in the area to determine if anyone heard or saw anything suspicious over New Year's Eve and into the early hours of New Year's Day.
The area has a large number of flats and apartments - so detectives believe that a significant number of people must have been in the area over the past 24 hours.
A large number of revellers were also in the area last night as people celebrated New Year's Eve with the general vicinity having a number of pubs and restaurants.
Gardaí also want to confirm the last known movements of the deceased.
Investigations are ongoing