The Chekhovian Short Story
Harold Bloom, in his study How to Read and Why, argues that the modern short story tends "to be either Chekhovian or Borgesian," that is, in the tradition of the short stories of either Anton Chekhov or Jorges Luis Borges.
Though Raymond Carver's most frequently-cited influence was Hemingway, it is indeed Chekhov's short stories that provide the best understanding of Carver's work. There are a few qualities that Chekhov pioneered in his work that Carver emulates, consciously and perhaps also unconsciously. (Though, it should be said, the connection is hardly a new discovery, and was frequently acknowledged by Carver.)
These qualities include:
1) Impressionism: Chekhov's stories fit within the style of impressionism, an art style wherein the artist is more concerned with capturing a subjective experience rather than realistically depicting the world. Carver's work is firmly grounded in the realist tradition, but the perspective of people and the world is often more palpable than the plot details. In fact, many stories leave out details, forcing the reader to piece the plot together from hints. This is a technique used by Chekhov as well.
2) Understatement: Chekhov's talent for understatement is one of his most lauded. Chekhov's stories are frequently very short – often just a couple of pages – but suggest far more than what is explicitly stated. In a similar way, Carver's narrators frequently lack the vocabulary to express the depth of their disillusionment, which leaves the reader to 'read between the lines' to recognize the full depth of the story.
3) The use of 'epiphanies': Both Chekhov's stories and plays feature characters who have epiphanies about how their lives need to change; frequently, these epiphanies are not followed through on. Several stories in this collection have epiphanies – Marge almost confronting Harley in "The Bridle," the communion with the baker in "A Small, Good Thing," or the ending of "Cathedral" – but most hint that the epiphany might not lead to long-term change.
4) A mixture of pessimism and humor: Chekhov's worldview is often described as 'tragicomic,' since he tends to position humans as alone and powerless, while showing their plight in a comic way. Most stories in this collection suggest the theme that we can never escape ourselves, and that we will cause our own unhappiness. And yet there are many uses of humor, like the narrator's clever meanness in "Cathedral." Carver's frequent use of irony underscores how silly symbols can suggest great pain, like the earwax in "Careful."
Carver is certainly an original artist, but time with Chekhov's best stories – start with "The Lady with the Pet Dog" or "The Duel" – can give great insight into the tradition that informed Carver's work.