VENICE.- During a 1976 lecture at Harvard University, conductor and composer Leonard Bernstein said, “A work of art does not answer questions, it provokes them.”

It’s fitting that Bradley Cooper opens his new movie about the musician with that same quote: Ever since the teaser trailer dropped for “Maestro,” which Cooper directed, co-wrote and starred in, all sorts of questions have been flying. And though Bernstein may have been hesitant to answer queries about art, I feel no such reluctance: Having caught the movie Saturday during its debut at the Venice Film Festival, I’m ready to fill you in on everything you might want to know about “Maestro.”

What’s it about?

Due on Netflix in December, “Maestro” tracks the exceptional but complicated life of Bernstein, best known as the composer of works such as “West Side Story” and widely considered America’s first great conductor. When we meet Bernstein, he’s about to get his big break as the fill-in conductor of the New York Philharmonic, news he excitedly shares with the handsome musical collaborator (Matt Bomer) who is still naked in his bed. But as Bernstein’s profile rises, he finds himself beguiled by Felicia Montealegre (Carey Mulligan), an actress with an exotic Chilean accent and a laugh like a musical trill.

“The world wants us to be one thing and I find that deplorable,” Bernstein confides to her. Pressured by friends to live his life and work in a way that is “clean,” Bernstein marries Montealegre, who accepts his occasional dalliances with men so long as he’s discreet. The problem is, he isn’t. (Alongside “Oppenheimer” and the forthcoming “Ferrari,” you could file “Maestro” under “Movies About Major 20th-Century Figures Who Might Have Fooled Around a Little Too Much.”)

So is it a biography of Bernstein?

If you refer to “Maestro” as a biopic, expect a sternly worded email from the movie’s reps. The film is actually a love story, they insist. It’s true that the 27-year marriage between Bernstein and Montealegre is the primary concern.

It’s also true that “Maestro” doesn’t play by traditional biopic rules. This isn’t a cradle-to-the-grave record of Bernstein’s artistic accomplishments, which mostly occur in the background or in the ellipses between scenes. Even his iconic “West Side Story” score is heard only once, as the unexpected soundtrack to a domestic scene late in the movie. You do get to see Bernstein conduct in a virtuoso long take, but the film’s most notable musical sequence is a dream ballet. (Between that scene and the “I’m Just Ken” number from “Barbie,” cinematic dream ballets are really having a moment.)

What’s up with that fake nose?

After Netflix released the teaser trailer for “Maestro” in mid-August, the prosthetic nose Cooper wore to play Bernstein was criticized on social media, and some questioned why a non-Jewish actor was playing such a famous Jewish figure to begin with. In response, the Bernsteins’ three children issued a statement, saying, “It happens to be true that Leonard Bernstein had a nice, big nose. Bradley chose to use makeup to amplify his resemblance, and we’re perfectly fine with that.”

Leaving issues of propriety aside, how does Cooper’s fake schnoz look in the movie? It helps that the first time “Maestro” shows Cooper is during a brief flash-forward set near the end of Bernstein’s life: The nose is only one element of the frankly astonishing old-age makeup he’s got on, so it’s hardly the first thing you’d notice. But when the film flashes back to Bernstein as a young man, the prosthetic proves intermittently distracting. It’s both too much and not enough: Unlike the fake nose in “The Hours,” which really did render Nicole Kidman unrecognizable, young Bernstein just looks like Bradley Cooper wearing a big beak.

Why is Carey Mulligan billed first?

The trailer for “Maestro” gives Mulligan first billing over Cooper, and the initial poster for the film features only her, which led observers to wonder if “Maestro” would be told primarily through Montealegre’s point of view.

It isn’t. Though Mulligan has way more to do than some of the other suffering spouses in films this year, Cooper edges her out decisively when it comes to screen time. (Even if you regard “Maestro” as practically a two-hander, it’s he who has the upper hand.) But hey, the billing was a nice gesture, at least! Or maybe Cooper, who is cited five separate times in the credits for “Maestro,” simply felt he should give his name a brief reprieve.

Will ‘Maestro’ be an Oscar contender?

Cooper’s feature directing debut, “A Star Is Born” (2018), was nominated for eight Oscars and won one, for its original song, “Shallow.” Can “Maestro” prove to be similar Oscar bait and even snag Cooper the best-director nomination he missed out on a few years ago?

Raves from industry trades Variety and the Hollywood Reporter will help raise the film’s awards chances, though cooler reactions from IndieWire and Vulture suggest not all critics will be in lock step. And since the SAG-AFTRA strike inhibits Cooper’s ability to promote “Maestro” — he wasn’t even able to appear at the Venice news conference or premiere, since guild rules currently prohibit actors from doing press for big-studio projects — he’ll have to rely on others to make the case for him.

But it’s hard to deny the bigness of those lead performances, and after “A Star Is Born” best-actor nominee Cooper lost the Oscar to a prosthetics-laden Rami Malek playing a real person, maybe it’s Cooper’s turn to have that kind of award-magnet role. It’ll be a crowded field full of contenders including Cillian Murphy (“Oppenheimer”) and Leonardo DiCaprio (“Killers of the Flower Moon"), but you can’t count out a nine-time nominee like Cooper: If he gets in, I suspect it will be by much more than a nose.

This article originally appeared in The New York Times.