Many years ago, before I was married, I was fortunate enough to live in one of the elegant old mansion blocks in the Copenhagen district of Frederiksberg, a stone’s throw from the immaculate lawns and shaded avenues of Frederiksberg Gardens. My apartment was the envy of my friends, with its parquet floors, high ceilings and ornate cornicing, but, as so often with these things, there was a downside.

I lived on the fourth floor to the right, directly above Mrs Vonnesbech, a retired headmistress with too much time on her hands. There were a few families in the building, an air hostess who was rarely at home, and a couple of single men like myself, but Mrs Vonnesbech, who knew that I was a lawyer and worked at the Ministry of Justice, had got it into her head that she and I ought to stick together as the only people there with what she called ‘proper professions’.

I may inadvertently have encouraged her by agreeing to leave my daily newspaper on her doormat in the evenings once I had finished with it. In any case, she sought every opportunity to strike up a conversation with me, and if this had seemed neighbourly at first, it soon became a source of deep resentment on my part.

Mrs Vonnesbech had many preoccupations, such as the ineptitude of the social-democratic government or the frequency of our rubbish collections, but she took a particularly obsessive interest in the man who lived in the apartment above mine. No one knew anything about Schliemann, apart from his name, which was evident from the brass plate on his door, and that he played the piano.

Schliemann had offended Mrs Vonnesbech by evading her attempts to discover anything about him.

Despite living a mere floor apart, he and I never passed one another on the stairs. Schliemann kept strange hours, often leaving or returning to his apartment early in the morning. I used to imagine that he worked as a pianist in some glamorous, smoke-filled jazz club in the city – a young man’s fancy.

Certainly, Schliemann often seemed mortally tired on returning home. His tread on the stairs was slow and shuffling, as if he could barely drag himself up the steps.

Though he often played the piano late at night, I didn’t mind, as he was an excellent musician with a fondness for Chopin’s preludes, and the rather mournful, meandering tunes seemed to me to go perfectly with the grand surroundings of the apartment building.

Mrs Vonnesbech, however, would talk scathingly about Schliemann, complaining that he always left the street door open, sending a chill up the stairwell whenever he passed.

‘Now, now, Mrs Vonnesbech, let’s not go making unfounded accusations,’ I protested. ‘Poor Schliemann, it might not be him at all.’

‘Oh, but it is,’ she said. ‘And he knows I know, for he hides whenever I try to catch him on the stairs, and pretends he is not at home when I knock on his door. He never answers my notes.’

I began to loathe returning to my flat in the evenings. Mrs Vonnesbech’s diatribes would leave me in a cloudy mood even on the sunniest of days. I tried to vary my times of arrival, even removing my shoes and tiptoeing past her door, but Mrs Vonnesbech never failed to intercept me.

One evening I was particularly exhausted and had resolved to confront her about her unwanted attention, but no sooner had I entered from the street than her flustered face appeared over the banister. Despite my best intentions, I found myself being dragged into her apartment.

There was a smell of dinner, and on her dining table lay scissors, newspapers and her reading glasses. My heart sank. Mrs Vonnesbech was a keen amateur historian, and I had by then been subjected to many a tedious lecture on town planning and local dignitaries.

‘Now, Mrs Vonnesbech, I’ve had a long day in the office and I really don’t think …’

‘Wait,’ she said, pushing an old photograph under my nose. ‘Tell me what you see.’

‘It’s a picture of our building, years ago. There are no cars parked in the street, and there’s a tobacconist’s where the corner shop is now. When was it taken?’

‘1882. Fifteen years after the building was completed, but that’s not it. Look at the windows.’

‘There is something, on the top floor, there. Looks like … could it be someone’s face?’

‘Yes,’ she said triumphantly.

I was confused. What was so unusual about a face in the window?

‘Now look at this one from 1891.’

‘The shop sign has changed, and there’s a horse-drawn milk cart in the road.’

‘No, not that; look at the windows again.’

‘Ah yes, I see, another face.’

‘No, the same face.’

‘Maybe, could be, but so what?’

‘Does it not strike you as odd?’

‘Not especially, no. It’s perfectly normal for people to be standing by their windows looking out, especially if they are waiting for someone, perhaps a spouse or a child returning home. Now if you’ll excuse me, I’d like to catch the end of the evening news.’

She was dejected and I had to see myself out. I felt a vague sense of guilt in the next few weeks at having so roughly rebuffed her, for she did not speak to me in all that time, but I was also pleased with myself for having put her in her place.

Of course, no such thing had occurred. One evening, about three weeks after she first showed me the photographs, I found Mrs Vonnesbech waiting for me when I returned from work.

‘You won’t believe this,’ she said, once more dragging me into her apartment.

On her dining table there was now a stack of books and papers. The room was unkempt and smelled of the sweat that had stained Mrs Vonnesbech’s shirt under the armpits and gathered on her top lip.

It is necessary to pause here to stress how extremely unusual it was for Mrs Vonnesbech to be in such a state, and it may help to explain what followed. I have never before, and never in all the years since, met anyone as fastidious as Mrs Vonnesbech. Whether it was a legacy from her days as a headmistress, I could not say, but she had always been immaculately turned out in a blouse and skirt with well-polished, brown lace-up shoes, with her grey hair swept neatly into a bun. She abhorred dirt and untidiness, protesting with angry notes pinned to the noticeboard in the stairwell whenever some poor soul had left a stain on the stairs or a bag of rubbish outside their front door.

To find her now in this dishevelled state was alarming. She stared at me with a wild, almost manic look in her eyes, and her voice was fast and breathless.

‘I spent the past three weeks at the state library looking through books. I found eleven photographs of this building, from 1872 to just three years ago. Take a look,’ she said, passing me the magnifying glass.

On each of the photographs, there appeared to be a face in the window of the top floor, a pale disc with dark hollows for eyes and a wide-open mouth. The angle varied, and the features were never clear enough to tell who it was, but there was someone there, I had to give her that.

‘Well?’ she said.

‘I admit it’s rather odd. There is no way to explain it that I can think of, just one of those strange coincidences. Each time a photograph has been taken, someone happened to be looking out of exactly that window.’

‘It’s no coincidence, it’s Schliemann.’

‘Come now, Mrs Vonnesbech, Schliemann cannot be over a hundred years old.’

She stared at me through her thick spectacles till I stopped laughing. It was obvious that she had gone quite mad, a woman of intelligence having lived alone for too long with nothing to occupy her inquisitive mind.

‘Now someone like you, working at the Ministry of Justice,’ she said, ‘you’re bound to have contacts in the police who can investigate the photographs, enlarge them, analyse and so on.’

‘What?’

‘Think about it,’ she said. ‘Have you ever seen Schliemann receive post, or a visitor? Have you ever actually seen him at all?’

‘No, but that doesn’t mean …’

Mrs Vonnesbech was standing in the middle of the floor, her hands waving about, strands of grey hair flying loose.

‘There is something about him. Something very wrong, I know it. Now if only you would ask a colleague of yours to take a closer look.’

I shook my head, but she was undeterred. ‘There is another thing. I need access to your apartment to see if I can hear Schliemann up there, or somehow work a probe through the floorboards. I must know what’s going on.’

‘Hang on a minute.’

‘It’s either that, or going the other way, through the loft.’

I was exasperated and used a harsh tone with her, which I now regret bitterly. ‘Now listen here, Mrs Vonnesbech. It’s plain that you are obsessed with Schliemann, and I want no part of it. As far as I am concerned, he’s a decent neighbour who has never done anyone any harm, whereas you have made my life a misery by forcing me to listen to your banal delusions night after night after night. From now on, I would like you to leave me alone.’

I never spoke to Mrs Vonnesbech again. What happened next is something I have pieced together subsequently, and some of it is guesswork.

It is safe to conclude that Mrs Vonnesbech did not give up on her theory, at least not straight away. I know as much, because the next day while I was at work, she dropped an envelope through my letterbox with the photographs she had found of our building. On a handwritten note, stripped of pleasantries, she had repeated her suggestion that I get them properly analysed.

A week or so later, she dropped another photo through my letterbox. I could tell that it been taken recently, as I saw my own bicycle chained to the lamp post outside. It was somewhat blurred, but Mrs Vonnesbech’s point was nevertheless clearly made. There was a face in the window of the apartment upstairs from mine.

I had a university friend in those days who had joined the police when I began working at the Ministry of Justice. I would like to think now that some part of me was genuinely curious about the photographs, but mostly I wanted to rid myself of my guilty conscience at the way I had treated Mrs Vonnesbech. So I dropped the photos off with my friend at the police yard, told him there was no rush, and left it at that.

Very soon afterwards, it transpired that our apartment building needed a new roof. One day, a notice appeared in our stairwell, announcing an extraordinary tenants’ meeting. As leaseholders, we were called to vote on the work, the cost of which we were being asked to share.

As a novice lawyer on a modest salary, already struggling to pay the rent on an apartment I could ill afford, this was impossible for me. I moved out the same month, and so did not attend the tenants’ meeting.

I later learned, from one of the other single men in the building, that Mrs Vonnesbech, who had taken it upon herself to act as spokesperson, became incensed that Schliemann did not turn up. Everyone would have to pay their share, she maintained, with no exception. Apparently, it was all they could do to stop her from marching up to Schliemann’s apartment and breaking down the door.

What exactly did Mrs Vonnesbech do between that evening and five days later when the dreadful thing happened? I had seen how agitated she had become before I moved out and would not have put anything past her, including camping out on Schliemann’s doorstep.

It was the air hostess who found the body in the small hours of the morning, on returning home after a long-haul flight from the Far East. It said afterwards in the newspaper that Mrs Vonnesbech was lying at the bottom of the stairs in a pool of blood, several bones in her body broken, including her neck.

On the fifth floor, they found that the retractable ladder to the loft space had been pulled down, the hatch left wide open. The coroner concluded that Mrs Vonnesbech, a woman of some girth and advanced years, had lost her footing and fallen unluckily through the gap between the stairs. It was assumed that she had been on her way to inspect the loft in advance of work starting on the new roof.

When I read the article, I got a cold feeling all over. I knew that Mrs Vonnesbech would have been trying to get into the loft space in order to spy on Schliemann. I also felt certain she would not have lost her footing. She was as strong as a bull, a keen rower who had once been a PE teacher.

Months later, my friend from the police called me about the photographs. I had quite forgotten about them and was trying to push Mrs Vonnesbech to the back of my mind and get on with my life.

‘Sorry it’s taken a while,’ my friend said. ‘The first tests we ran were inconclusive, but I got curious, so I sent the pictures off to Germany for further analysis. Only got them back today.’

He laughed heartily. ‘Very clever,’ he said. ‘You almost had me there. But tell me, how did you do it? How did you put that ghastly face in there, the same face, in all those photos, years apart?’

I forced myself to laugh. ‘That’s for me to know, and you to find out,’ I said. ‘Glad you enjoyed the joke, my old friend.’

I cut him off, and, to my infinite shame, never spoke to him again. He is dead now and, for all I know, he never learnt the truth.

In all these years, I have never told anyone what happened back then, not even my wife. May God forgive me, I was, and still am, a coward. I had just embarked on my legal career, and knew full well that mysterious tales about a man upstairs who played the piano, and whom no one had seen except in photographs, would do me no favours at all.

You may ask, Why tell the story now, thirty years later?

For many years, I avoided Frederiksberg, and declined any engagement, social or professional, near the gardens or the building where I used to live. But the memory of Schliemann eventually faded, as these things do, and in time I managed to persuade myself that what happened had a logical explanation, however tragic, and now belonged safely in the past.

It was last Saturday afternoon, when, on my way to collect my wife from lunch, I found myself on the very road in Frederiksberg where I used to live. When I passed the apartment building, my eyes drifted upwards subconsciously, if only for a second, and I saw the face in the window on the fifth floor, clear as day, staring at me with dark intent, the cheeks sunken beneath the sharp, pallid cheekbones.

If you don’t believe me, and you happen to be in Copenhagen, go and see for yourself. You can’t miss the place; it is the most imposing apartment building in Frederiksberg. Look up at the dormer windows set into the roof, to the right of the entrance door. Schliemann will be there waiting, his face set back from the glass, partly obscured by a curtain, the dark hollows of his eyes staring out at someone or something that is never coming back.