The film is a live-action cyberpunk adventure based on a Japanese manga comic, and you could see her giant-eyed look as a knowing declaration of intent: here is a tribute to the source material, and one that millions of manga fans will get in a flash.
It seems to capture a moment - underscored by news that the British Museum will be opening an exhibition dedicated to Japanese comics this year.
Manga and its celluloid cousin anime are now mainstream in the West. They have left the comic-shop basement and entered the museum and the multiplex.
Japanese, with its pictographic written language, is a visual culture; and comics have long had a place in the mainstream of Japanese society that (leaving aside the last decade or so of wham-bang superhero adaptations) they still do not have in the West.
A statistic cited by reputable scholars states that Japan uses more paper for comics than for toilet paper.
There are comics to cover every imaginable aspect of life, from cookery and baseball to mothers-in-law. Government white papers have even been released in manga form.
Manga (in Japanese it means something like "whimsical pictures") and anime can seem baffling to many Westerners - not least because of the disproportionate attention given to scantily clad schoolgirls and the semi-mythic proliferation of "tentacle porn", which I would suggest you do not Google - but the irony is that they have, if you go back, Western roots.
In fact, they derive from that staple of the dentist waiting room, Punch. Though the earliest Japanese comics are usually said to be the satirical Choju Giga scrolls, drawn by a Buddhist priest in the 12th century, their modern form owes a lot to Western influence.
After Japan was forcibly opened up in 1853 by the American Commodore Matthew Perry and his military/diplomatic fleet, its growing expat community started to consume a version of the British magazine called The Japan Punch - and it had a considerable impact on the local cartooning community.
Brushes gave way to pen and ink, and the exaggerated, cartoony stylings of Mr Punch seeped into the local idiom.In anime, the story was similar.
Japanese film studios, which had been producing animated films since the early 20th century, got a shot in the arm with the global success of Walt Disney, and Osamu Tezuka, the creator who invented Astroboy and is often called "the god of manga", adopted and developed a number of Disney's techniques.
Indeed, the convention for anime characters to have giant eyes - what cognitive psychologists associate with the "kinderschema", that is, the characteristics that make something cute - is usually traced back to Tezuka's influence; and through him, to Western animation in the big-eyed form of none other than Betty Boop.
From the middle of the 20th century onwards - and with dazzling speed as we entered the 21st century - manga and anime have re?exported the influence. Godzilla, Power Rangers, Pokemon, Final Fantasy - all would have been impossible without anime. The cyberpunk worlds of William Gibson and the Ridley Scott of Blade Runner are deeply Japanese.
And a number of live-action blockbusters - such as Pacific Rim, which is to be made into an anime series or Transformers - are either lifts from anime or, as in Ghost in the Shell or Alita: Battle Angel, are direct adaptations.What are the main characteristics of anime works?
No generalisation will cover such a vast area - Japan has more than 400 anime studios - but the ones that are most eagerly seized on and recycled by the West tend to be cyberpunk and post-apocalyptic adventure stories.
Giant robots - such as the Mobile Suit Gundam series - have been a staple of Japanese animation since the Seventies. Blasted cityscapes are common; as are kaiju (giant monsters) such as those from Godzilla and Pacific Rim. It's not hard for the amateur cultural critic to make some connections between manga and anime tropes and Japan's national preoccupations and traumas.
Katsuhiro Otomo's Akira, whose 1988 screen adaptation became one of the most celebrated of all anime works, opens with: "At 2.17pm on Dec 6 1992, a new type of bomb exploded over the metropolitan area of Japan."
That's going to resonate in a country whose history is uniquely marked by tragedy in Hiroshima and Nagasaki. (It's worth remembering that one of the most enduring artistic responses to the attacks, by Hiroshima survivor Keiji Nakazawa's Barefoot Gen, was in manga - and later adapted as an anime movie.)
The post-apocalyptic cityscape is an obvious export from the country that most recently witnessed actual post-apocalyptic cityscapes.
Hi-tech dystopias are readily available in a country whose relationship with technology has been so thorough and, at the same time, so mixed. And it's perhaps easy to see why, in manga and anime, radiation would produce terrifying monsters (rather than cuddly superheroes).
Likewise, why a country with such a strong military history that, since the Second World War, is not allowed to have an offensive military force, might find an outlet in fantasies of battle robots and giant mech-suits.
Another thing that's striking is the prevalence of manga in Japanese society. We traditionally think of comics as for children. So it can be disconcerting to see how manga and anime juxtapose an apparently childish style with some extremely adult subject matter.
Anime can be extraordinarily violent, and its characters - doe-eyed schoolgirls with tiny skirts and inflated busts - both cartoonish and highly sexualised. It tends to violate standard Western norms in that respect. Anime is closer to comics than Western animation.
They feature fixed, yet beautifully detailed, hyperrealistic backgrounds on a huge scale, and across them, parades a cast of 2D, highly stylised characters. In combat they appear mid-leap while bangs and clashes judder behind them.
Explosions are not hectic orange percussions but blooms of light or smoke.So it takes some tuning in. But these styles contain glories, and they are coming ever more unfiltered to Western audiences - at last - equipped to read and revel in them.
• Alita: Battle Angel opens in cinemas on February 14.
