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Herein, some of "La mujer sin cabeza's" critical champions (and a few detractors at the bottom):
In his review, the New York Times' A.O. Scott delves deep into the thematic aspirations of the film, calling it "a meditation on Argentina’s historical memory. It subtly compares Verónica’s silent disavowal of responsibility for any crime she might have committed with that country’s silence during its dictatorship, when suspected dissidents disappeared."
Film Comment's Editor-at-Large Kent Jones has been a supporter of the film since Cannes (and actually, of every film Martel has ever made since they have all been shown at the NYFF). In this report that appeared last year, he discusses Martel's "forensic" style: "Martel excitingly confines herself to her heroine’s traumatically realigned viewpoint (the scope frame is used in the most exacting fashion, in conjunction with the soundtrack, to suggest a hallucinatory mental space both within and without María Onetto’s character)."
The venerable J. Hoberman, writing for the Village Voice, focuses on the film's texture: "As dense and fluid as Martel's movie is, the viewer—like the protagonist—is compelled to live in the moment. And a rich moment it is. With its shallow focus, chiaroscuro lighting, off-centered wide-screen compositions, and constant background noise, The Headless Woman teems with life."
On indiewire, Eric Hynes seems to withhold judgement, but his review is thoughtful nonetheless. He interestingly talks about how Martel's approach to class has evolved since her first film: "Martel’s approach to class in “The Headless Woman” is both more subtle and forceful. Fewer racist complaints about filthy, shady “Indians” are heard than in “La Cienaga” and “The Holy Girl,” but Vero’s entire existence depends on and is restored by privilege. A young boy whose corpse is found clogging the canals—Vero’s victim?—remains unidentified while Vero’s identity is exhaustively retraced. Even her guilt (itself a privileged emotion), though it prompts her to small generosities toward house staff and day laborers, assumes an interchangeability of the underclass."
Glenn Kenny, from Some Came Running, wrote about "La mujer sin cabeza" last year in Cannes: "Throughout, Martel places the character in shallow focus widescreen close-ups; therein, those people in her periphery—generally servants, workers, and so on—are diffused, hazy. It's an oblique way of reflecting on contemporary class relations, but it's apt, and in point of fact this is one of the few films in the largely-socially-conscious Competition that reflects on class relations as such."
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For the New Yorker, Richard Brody (why not Denby or Lane?) writes: "Martel tries to have it both ways, attempting to construct a rich reality by accretion of ordinary and realistic detail, while stacking the narrative deck so rigorously that the characters evaporate into symbols almost upon their appearance."
Slant's Akiva Gootlieb, argues that: "Films that try to convey a state of disorientation live and die by their central metaphors, and the one that lends Lucrecia Martel's The Headless Woman its title is certifiably lame."
I guess you can't win 'em all!