Aira continues Borges, which is, I suppose, inevitable, coming as he does from Coronel Pringles, a little town in la provincia de Buenos Aires. (I passed through it by bus, long ago.) In a brief preface, Bolaño also suggests the influence of Witold Gombrowicz, the enfant terrible of Polish/Argentinean literature. I don't hear Gombrowicz, frankly—but I don't hear much that Bolaño hears, and that's no fault of Bolaño's.
I do hear Dostoyevsky.
If a bastard child of Dostoyevsky and Borges doesn't trigger your interest, then you can't be helped.
Consider, for instance, this line—a brilliant summary of the dilemma of the artist in the modern age:
The variations revolved around a curious impossibility: how could he communicate the proposition “I am a monster”?The influences one hears are to Aira's credit. Bolaño claims Aira is "one of the three or four best writers working in Spanish today." After reading this little book, I don't doubt it.