By Imogen Foulkes
BBC News, Geneva
Mr Polanski's wife Emmanuelle Seigner is said to be shocked by his arrest
Roman Polanski's arrest in Zurich at the weekend has caused headlines around the world and anger among many.
But legally, Switzerland's extradition agreement with the United States is clear.
The US had issued an international arrest warrant for Mr Polanski. US officials apparently pointed out that the film director would be on Swiss soil on Saturday, and asked the Swiss authorities to detain him.
Switzerland's Justice Minister Eveline Widmer-Schlumpf did not hesitate.
"We have an agreement with the US to apprehend those wanted for offences," she said.
"When we knew Mr Polanski was here and the US asked us to act, it was our duty to do so."
But that does not really explain why Switzerland chose this particular moment to act.
Roman Polanski is a regular visitor to Switzerland. He has a holiday home in the resort of Gstaad where he likes to ski.
Many Swiss - especially those who turned up at Zurich's film festival expecting to see Mr Polanski receive a lifetime achievement award - feel the police action ordered by the government was clumsy, even cruel.
"How the Swiss can invite him to an official event to receive an award, and then arrest him, I can't understand it," said one visitor. "It's ludicrous, ridiculous."
"I think it is shameful, bothering an old man like that," said another. "I am ashamed to be Swiss."
Swiss political parties on the left and the right have their doubts too.
"For me this arrest is impossible to understand," said Ueli Leuenberger of the Green Party. "He was an honoured guest in our country."
On the right, Toni Brunner of the Swiss People's Party expressed anger at what he sees as Switzerland's eagerness to carry out US instructions.
Swiss Justice Minister Eveline Widmer-Schlumpf says it was her duty to act
"It's ridiculous and just shows what happens when we try to serve foreign masters," said Mr Brunner.
But despite the loud chorus of disapproval, many other Swiss believe the events which led to Mr Polanski's arrest should not be overlooked.
"What we are talking about is the statutory rape of a 13-year-old girl, one of the most serious crimes there is," said Christophe Darbellay of the Christian Democrats.
"I think Mr Polanski should be extradited to the United States as soon as possible."
But speed is unlikely to be a factor in this case.
Lawyers are already being wheeled into position for what is likely to be a long and complicated legal process.
Mr Polanski has now appointed a Swiss lawyer, whose first action could be to appeal against the original decision to arrest him.
Meanwhile, the film director's French lawyer is expected in Zurich later on Monday, together with Mr Polanski's wife Emmanuelle Seigner, who is said to be shocked by his arrest.
The French culture minister has suggested France would challenge any attempt to extradite Mr Polanski.
The US has 60 days to serve the extradition request, but even then, Mr Polanski can challenge it in the Swiss courts.
It is a process which could take weeks, more likely months.
Swiss precedent shows that the subjects of extradition requests are normally kept in detention.
Although the Swiss justice ministry has said bail for Roman Polanski cannot be excluded, if bail is granted the conditions are likely to be very strict indeed.
After all, Mr Polanski's record on bail is not a good one - 31 years ago he skipped bail in the United States and fled to France rather than be sentenced in a US court.
That is the reason he is in detention in Zurich today.