who is the autor of the book thar Diego was going to borrow to David?

Interesant question, it was a Neruda's book. If you pay attention you can even see the title: "20 love poems and a Desesperate Song", It´s a very interesting scene because Diego, with that book, wants to be sure that David must go back hit him, even if it's only to return the book.

Greets!

Silence girl, if you ask at the beginning of the movie, that one I don't remember which author, but if it is the book he got from Diego by the half end of the movie, that book was Paradiso, by Jose Lezama Lima.

I hope this helps.

No, no, no... At the beginning of the movie, the book that Diego offers to David is Conversación en la Catedral, by Vargas Llosa. In the book from which this movie is based, the book is a different one, though still a Vargas Llosa title: La Guerra del Fin del Mundo (The War of the End of the World). This actually helps the reader to understand when the story is taking place.

But there's a ton other references to books, authors and artists, so I don't know for sure if this is the answer to your question. But I can tell you for a fact that Neruda has no mention or appearance of any kind or form in the movie.

I watch the movie a few hours ago and I'm sure the book you are asking for is Mario Vargas LLosas' "Conversación en la Catedral" (I dunno the title in English, sorry for that).