Jorge Luis Borges, the Argentine short-story writer, poet and essayist who was considered one of Latin America's greatest writers, died yesterday in Geneva, where he had been living for three months. He was 86 years old. Mr. Borges died of liver cancer, the executor of his estate, Osvaldo Luis Vidaurre, said in Buenos Aires. While almost unknown outside Argentina before 1961, his stories, punctilious in their language and mysterious in their opaque parodoxes, later attained a modest following in the United States, a following that grew steadily to international proportions. His writings explored the crannies of the human psyche, the fantastic within the apparently mundane, imaginary bestiaries and fables of obscure libraries and arcane scholarship. His prose provoked the literary imaginations of general readers, scholars and critics, and many hailed him as the most important Latin American writer of this century. Among his works of fiction that have appeared in the United States are ''Ficciones,'' ''The Aleph and Other Stories'' and ''Labyrinths,'' all published in 1962, and ''A Universal History of Infamy,'' in 1971. Among his collections of essays available in English are ''The Book of Imaginary Beings'' (1969) and ''An Introduction to American Literature'' (1971). ''Selected Poems, 1923-1967'' was published in 1972 and ''In Praise of Darkness,'' which consists of poetry and short pieces, in 1974. In 1975 John Updike wrote that Mr. Borges's ''driest paragraph is somehow compelling.'' ''His fables are written from a height of intelligence less rare in philosophy and physics than in fiction,'' he said. ''Furthermore, he is, at least for anyone whose taste runs to puzzles or pure speculation, delightfully entertaining.'' Moreover, Mr. Updike insisted, ''For all his modesty and reasonableness of tone, he proposes some sort of essential revision in literature itself.'' It is, the historian and philosopher George Steiner wrote, perhaps something even more: ''Borges's universalism is a deeply felt imaginative strategy, a maneuver to be in touch with the great winds that blow from the heart of things. ''When he cites fictitious titles, imaginary cross-references, folios and writers that have never existed, Borges is simply regrouping counters of reality into the shape of possible other worlds. When he moves, by wordplay and echo, from language to language, he is turning the kaleidoscope, throwing the light on another patch of the wall.'' One of his earliest short stories, ''Pierre Menard, Author of the Quixote,'' compressed this embrace of language and illusion, foreshadowing the tenor of his later work. In the story, written in 1938, Mr. Borges proposed, in short, an extreme examination of T. S. Eliot's dictum that each new work of art alters the perception of previously existing works of art. For Mr. Borges, the short story - a literary form ''whose indispensable elements are economy and a clearly stated beginning, middle and end'' -was the most compelling form. Once he wrote: ''In the course of a lifetime devoted chiefly to books, I have read but few novels and, in most cases, only a sense of duty has enabled me to find my way to their last page. I have always been a reader and rereader of short stories.'' Beginning in 1927, when he had a series of operations on his eyes, Mr. Borges was increasingly afflicted by blindness, which ran in his family. While he called it a ''slow, summer twilight,'' it did not impede his work. Jorge Luis Borges was born in Buenos Aires, in the house of his maternal grandparents, on Aug. 24, 1899. His father, of Italian, Jewish and English heritage, professed the law but, as Mr. Borges once wrote, ''was a philosophical anarchist - a disciple of Spencer -and also a teacher of psychology.'' His mother, of Argentine and Uruguayan stock, lived far into her 90's and translated William Saroyan, Nathaniel Hawthorne, Virginia Woolf and Herman Melville into Spanish. While he was very young, his parents moved to the northern suburbs of the capital, to Palermo, a place he later described as a slum. But it was not, he wrote, a slum in the American sense. It was, rather, a district where ''shabby-genteel people as well as more undesirable sorts'' lived. At the age of 6 or 7, the young Borges began to write. ''I was expected to be a writer,'' he recalled much later in life. He confessed that his first writing was modeled on classic Spanish writers, mostly Cervantes. The young man's first effort, ''The Fatal Helmet,'' was avowedly romantic - ''nonsensical,'' he later called it - and very much a stylistic derivative of Cervantes. In 1914 the family moved to Europe so that Jorge and his sister could attend school in Geneva. Jorge enrolled at the College of Geneva. In school, the young man was immersed in Latin, and outside it he tackled German. He learned to love the language through Heine and found his way to Schopenhauer, who was to be his favorite. ''Were I to choose a single philosopher, I would choose him,'' Mr. Borges wrote. ''If the riddle of the universe can be stated in words, I think these words would be in his writings.'' After Mr. Borges received his degree in Geneva, his family moved to Spain for a year, and it was there that his first poem was published. Called ''Hymn to the Sea,'' it was deliberately fashioned in the style of Walt Whitman. In 1921, he returned with his family to Buenos Aires, where he continued to write, experimenting with styles of prose that were either artificially Latinate or sodden with Argentine colloquialisms. Of his early works, he was relentlessly scornful. The ''real beginning'' of his career came, Mr. Borges wrote, in the early 1930's with a series of sketches called ''A Universal History of Infamy.'' In these, which ''were in the nature of hoaxes and pseudo-essays,'' Mr. Borges chronicled the lives of Lazarus Morell, who at once freed and imprisoned slaves; of Tom Castro, an implausible prodigal son; of the widow Ching, a pirate who terrorized the seas of Asia; of Monk Eastman, a New York gunman and ''purveyor of iniquities''; of Kotsuke no Suke, who refused to commit hara-kiri, ''which as a nobleman was his duty.'' With his next story, ''The Approach to al-Mu'tasim,'' written in 1935, the shape of many of his later stories was established. The story is a fictive review of a book purportedly published in Bombay. Mr. Borges invests the mythical volume with a genuine publisher and reviewer but, as he wrote later, ''the author and the book are entirely my own invention.'' In this early story, many of the basic literary elements that came to characterize Mr. Borges's style were apparent: a concern for history and identity; the central role of an obscure scholarly work; a maze of discourse laden with elaborate and Byzantine detail; footnotes; meticulous references to remote academic journals, and the presence of deliberately translucent paradox. Mr. Borges took his first full-time job in 1937 as the first assistant in the Miguel Cane branch of the Buenos Aires Municipal Library; he was paid about $70 a month, and was to remain there for nine years, completing his work each day in an hour or so and devoting the rest of his time to reading and writing. In this period, he wrote ''Pierre Menard, Author of the Quixote'' - a ''halfway house between the essay and true tale,'' he wrote. ''Pierre Menard'' led to a story of a strange world that displaces our planet - ''Tlon, Uqbar, Orbis Tertius'' - and then quickly to another and then the next, stories concerned with labyrinths and mirrors and encyclopedias that came to form the foundation of Mr. Borges's oeuvre. ''The Garden of Forking Paths,'' an anthology of short stories, was published in 1941, and three years later ''Ficciones,'' perhaps his most celebrated collection of short stories, went into print. In 1946, Juan Domingo Peron - ''a President,'' Mr. Borges wrote, ''whose name I do not want to remember'' -came to power. Not long afterward, Mr. Borges was named inspector of poultry and rabbits in the public markets. He found his selection for this new position baffling, and he resigned. By then, his reputation as a writer was secure, and he was asked to lecture on English literature at the Free College of Higher Studies and the Argentine Association of English Culture. After the Peron Government was overthrown in September 1955, Mr. Borges was appointed director of the National Library in Buenos Aires. The next year he became a professor of English and American literature at the University of Buenos Aires. With Adolfo Bioy-Casares, whom he met in the 1940's, he collaborated in writing a collection of short stories under the name H. Bustos Domecq. Mr. Borges once described the ''Chronicles'' of Bustos in 1967: ''These are articles written on imaginary, extravagantly modern artists - architects, sculptors, painters, chefs, poets, novelists, couturiers - by a devotedly modern critic. But both the author and his subjects are fools, and it is hard to tell who is taking in whom.'' By the late 1950's, Mr. Borges was completely blind. ''One salient consequence of my blindness was my gradual abandonment of free verse in favor of classical metrics,'' he wrote later. ''In fact, blindness made me take up the writing of poetry again. Since rough drafts were denied me, I had to fall back on memory. It is obviously easier to remember verse than prose and to remember regular verse forms rather than free ones.'' After he shared the Formentor Prize with Samuel Beckett in 1961, Mr. Borges's books began to sell increasingly well internationally, and he was invited abroad to lecture and to take up visiting professorships. Over the following years he traveled extensively in the United States and Europe, lecturing and receiving bouquets of literary awards. And though he was perennially a candidate for the Nobel Prize in Literature, it was denied him. It was perhaps less a concern to him than to others. After winning the prize in 1982, the Colombian novelist Gabriel Garcia Marquez said of Mr. Borges, ''I hope he receives it, and I still don't understand why they haven't given it to him.'' Some have insisted that it was Mr. Borges's aversion to politics, his unwillingness to criticize the repression of post-Peronist regimes - ''I suppose they are a necessary evil, for the next 50 years, or so,'' he said - that kept him from becoming a Nobel laureate. He was, however, sympathetic to the plight of mothers whose children were victims of death squads that were tacitly or actively supported by Argentina's military Government. ''I had my say about the disappeared,'' he told an interviewer. ''But what can I do? I'm an old man. What can they do to me? Torture me, eh?'' Mr. Borges led a hermetic, unworldly life. Seemingly fragile in his last years, as he leaned on a vertebral wooden cane, he was gentlemanly in manner and locution. With blindness he relied increasingly on assistants to read to him and to write what he dictated. Always Mr. Borges wrote and read, and perhaps it was, in the end, the latter that was paramount. ''To me, reading has been a way of living,'' he once said. ''I think the only possible fate for me was a literary life. I can't think of myself in a bookless world. I need books. They mean everything to me.'' During his lecture tours, he had a particular fondness for New Orleans. When he was not writing in his hotel room there, he was listening to jazz, invariably distinguished in his suit and tie from other jazz club patrons. ''My father told me a gentleman never goes in public in his shirt sleeves,'' he said, ''but I think these people are right to dress comfortably when it is hot.'' At the age of 68, Mr. Borges was married for the first time, to a childhood sweetheart, Elsa Astete Millan, the widow of a friend. It proved to be an unhappy episode, and they divorced three years later. He married Maria Kodama, his 41-year-old secretary and longtime traveling companion, a few weeks ago. In later life, Mr. Borges was not so happy as he had once been with Argentina and its capital. ''Buenos Aires is a dreary city now,'' he told an interviewer during the war with Britain over the Falkland Islands in the spring of 1982, a war he termed ''atrocious.'' ''I don't understand my own country. But the world is not meant to be understood by men. Every night, I dream. I have nightmares - of being lost, of being in an unknown city. I don't remember the name of the hotel, or I can't find my way home in Buenos Aires. Maybe I feel very lost because the world is meaningless.'' Yet Mr. Borges found meaning in his own work. At the end of his published conversations with the literary scholar Richard Burgin, Mr. Borges wrote: ''Through the years, a man peoples a space with images of provinces, kingdoms, mountains, bays, ships, islands, fishes, rooms, tools, stars, horses, and people. Shortly before his death, he discovers that the patient labyrinth of lines traces the image of his own face.''