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They walked through the cathedral with its blue-and-white candystripe nave, and then down a narrow lane until they reached the main street in the city centre, and finally found a table outside a small restaurant, overlooking the stream of people passing by.

Brock rubbed his hands. ‘We must try the local wine.’

He ordered a bottle while they examined a menu. Kathy settled for lasca, a speciality from nearby Lake Trasimeno, and Brock chose cannelloni. He asked her about her flight, her flatmates and half a dozen other unimportant things until the wine arrived. Then he raised his glass in a toast: ‘To absent friends.’

He didn’t offer an explanation, and she sipped at the wine, cool and fragrant.

He set down his glass and sighed. ‘Well, you’d better tell me what’s been going on,’ and she told him what she knew.

He shook his head when she had finished. ‘You can never be sure, I suppose, but I wouldn’t have thought him capable of it. Not like that. Dear God, it was savage, Kathy, the way her throat was cut. One single stroke, hard, decisive, absolutely unflinching. Her head was almost off. That’s not Geoffrey Parsons in a month of Sundays.’

She nodded agreement, and they sat in silence for a while until the waiter approached.

‘How did your paper go down, anyway?’ Kathy asked, brightening with the appearance of the food.

‘Oh, quite well. I’d been dreading the whole thing actually, but it was quite fun, as it turned out.’

‘Fun? A conference on catching serial killers?’

He managed a laugh, even though his mouth was full of pasta.

‘There was a good paper from a young American on chance and coincidence. I suppose somebody had to work chaos theory into it somehow, but he did it very well. He went back to Jung and Koestler and so on, and he had the most fascinating case-studies from America in which completely convincing but quite inexplicable coincidences appeared, which either misled or guided the police. With a long series of murders, of course, you get more opportunities for random things to creep in. But some of them were extraordinary, almost as if a third hand were at work. That’s the thing about life, I suppose, as against fiction. Quite strange but innocent coincidences do happen. You’re trying to construct a logic to lead you along the hidden thread, and you have to remember that sometimes the most beautiful alignment of events may actually be quite meaningless.’

Brock paused for another sip of the Orvieto wine, then continued.

‘Like the fact that the translation of Alex Petrou’s physiotherapy certificate was authenticated by the British embassy in Rome, not Athens — do you remember that? I thought at the time, What a coincidence, that’s where I’m going in a few weeks. Of course that was a meaningless coincidence, except that it did mean I could ask one of the Italian people I got to know here to try to find out what Petrou had been doing in Rome a year ago, just before he came to England. It wasn’t likely to be important, except that, when he came back with the answer, it suggested all sorts of other coincidences that were so beautiful, just like in the young American bloke’s paper, that I couldn’t resist finding out more.’

And finally Kathy realized that Brock wasn’t just wasting time, and with an enormous sense of relief she put down her knife and fork and stared at him. ‘You’ve found something out.’

‘Well, now, try this one. Petrou had been in Italy for six months. He had come from Greece and before that from the Lebanon, where his family had businesses. They finally quit Beirut about four years ago and moved back to Athens, where Alex trained as a physio. I don’t know why he came to Italy originally, but he got a job at a clinic, not in Rome but in Vicenza, up in the north. Now that is a rather promising coincidence, wouldn’t you say?’

Kathy shook her head, ‘Not off-hand.’

‘Vicenza was the home of Palladio, the sixteenth-century architect of the Malcontenta, the house which was the model for Stanhope House, the place where Alex was next going to show up.’

Kathy frowned doubtfully.

‘Too thin?’ Brock asked. ‘Well, let’s go on. The reason why Stephen Beamish-Newell established his clinic in the English Malcontenta was that his first wife found the place for him and was attracted to it because she recognized its source. And she recognized its source because she herself came from …’

‘Vicenza,’ Kathy whispered, feeling a prickling along her spine.

‘Right, Vicenza. Her family has lived in the city for generations. When she was eighteen they sent her to polish up her English at one of the language schools in Cambridge, and there she fell in love with a charismatic medical student. They married and eventually her family, being well off, provided the funds for them to set up their clinic. When her marriage fell apart, Gabriele returned to her family home and reverted to her maiden name, Montanari.’

‘And she was there when Alex Petrou was there?’

Brock nodded. ‘She still is.’ He took a folded sheet of paper out of his pocket and spread it on the table. It was a photocopy of a newspaper photograph of an attractive middle-aged woman in evening dress climbing the front steps of a building, accompanied by an older man in black tie. ‘Gabriele Montanari and her father, at their last public appearance, for a charity ball in Padua last Christmas.’

‘Do we know if she met Petrou?’

Brock shook his head. ‘No, we don’t know that. But, there’s a final coincidence: Papa Montanari turns out to be a shareholder of the clinic where Petrou was working.’

Kathy smiled. ‘They must have met.’

‘We do know that Petrou was getting himself into trouble in Vicenza. There were complaints to the authorities, suggestions of extortion. He lost his job at the clinic and would probably have been picked up by the local police if he hadn’t suddenly left Italy of his own accord. So what do you think of those coincidences?’

‘Compelling.’

‘I made a call home to Immigration and discovered that Petrou entered England at Dover, on a cross-Channel ferry from Calais. I’m also told that he bought the ticket at Calais, which suggests he didn’t have a through ticket on a train. In other words, someone might have driven him up from Vicenza and put him on the boat.’

‘What date was that?’

Brock consulted his notebook. ‘April Fool’s Day, last year. He started at Stanhope Clinic two days later.’

‘Quick work, if he didn’t have any contacts.’

‘Quite. And Stanhope isn’t exactly just off Piccadilly. It’s not the sort of place you’d run into by chance.’

They finished their meal and prepared to make a move.

‘Was she the absent friend you toasted?’ Kathy asked suddenly.

‘Who?’ Brock looked startled.

‘Gabriele Beamish-Newell’

‘Oh no. Someone else.’

‘Someone you’d like to be sharing a bottle of Orvieto with in some Italian hill-town.’

Brock gave a little nod and turned to go.

They reached Vicenza in the late afternoon. Brock had some scribbled notes by means of which he got them to the west gate of the old city, the Porta del Castello, and into the Piazza del Castello just beyond. There Kathy was introduced to her first Palladian building, the unfinished Palazzo Giulio Porto, in front of which they left the car and went in search of their hotel on foot. The owner of the Albergo Tre Re, when they eventually found it, advised them of a more suitable parking spot, and by dusk Kathy was unpacking her small bag in a tiny but charming room with a partial view of the dome of the cathedral. She thought of the elegant woman in the photograph and wished that she had brought more clothes.

The following morning they strolled down the main street, the Corso Andrea Palladio, until Brock, consulting his notes, led them down a side-street to a small square. There they established themselves at a table outside a small cafe and ordered breakfast. Brock pointed to a dark-brown building on the far side of the square. The Palazzo Trissino-Montanari. The family home.’