The showdown over whether Carnival Cruise Lines’ operations in Charleston violate city ordinances goes to the S.C. Supreme Court on Tuesday morning.

Oral arguments are scheduled to begin at 9:30 a.m. in Columbia.

The Preservation Society of Charleston, the Coastal Conservation League and downtown Charleston neighborhood groups filed the complaint two years ago alleging Carnival’s year-round cruises run counter to the city’s noise, public nuisance and sign ordinances.

The court dismissed the noise and signage claims earlier. But the justices requested new written arguments about whether the cruises are a public nuisance or violate local zoning rules.

That was based on the recommendations from a special referee.

Central to the arguments the justices want debated is whether municipal zoning ordinances apply to ocean-going vessels. Also, if so, are those ordinances superseded by state or federal laws?

The city, the State Ports Authority and Carnival want the case dismissed. The Supreme Court isn’t expected to issue a ruling immediately.

The dispute over cruises in downtown Charleston heated up in 2010 after Carnival permanently based its 2,056-passenger ship Fantasy at a berth near the City Market.

Neighborhood groups and environmentalists also have filed lawsuits to block the SPA from opening a new $35 million cruise terminal at the north end of Union Pier, claiming it will bring more tourists, traffic congestion and fumes to the historic district.