‘The Social Network’ is anointed by L.A. Film Critics Assn.

“The Social Network” was the big winner Sunday at the Los Angeles Film Critics Assn. Awards, nabbing the best picture prize, director for David Fincher (in a tie), screenplay for Aaron Sorkin and, in another tie, music for Trent Reznor and Atticus Ross.

With the exception of “Social Network” and “The King’s Speech,” which won the lead actor prize for Colin Firth’s portrayal of King George VI and runner-up nods for supporting actor Geoffrey Rush, screenwriter David Seidler and production designer Eve Stewart, LAFCA recognized more obscure titles and performances for the year, leaving many Oscar watchers at a loss for clues as to how those awards might play out.

Chief among those unusual choices was “Carlos,” the French film about Venezuelan revolutionary Ilich Ramírez Sánchez, which took the foreign language award and claimed the runner-up slot for best picture. Director Olivier Assayas shared the director trophy with Fincher.

Another offbeat choice was in the actress category, where Kim Hye-ja won for her role in the South Korean film “Mother,” a tale of a mother’s search for the killer who framed her son for murder. She beat out the young Jennifer Lawrence, whose portrayal of an Ozarks teen in “Winter’s Bone” has been one of the year’s most talked-about. Lawrence, considered an Oscar contender, was voted the runner-up.

In the supporting actor category, Niels Arestrup won for his role in the French film “A Prophet,” which was nominated last year for an Oscar in the foreign language category, and Jacki Weaver won for her part as the bubbly but ruthless matriarch of a crime family in the Australian drama “Animal Kingdom.”

“Toy Story 3” grabbed the prize in the animation category, while “The Illusionist” was granted runner-up status in a close vote, perhaps an indication of the third film that will land among the Academy Awards animation nominations — “How to Train Your Dragon” being the other likely contender.

In the documentary category, Chinese migrant story “Last Train Home” nabbed the prize, beating out graffiti artist Banksy’s “Exit Through the Gift Shop” and Davis Guggenheim’s popular film on public education, “Waiting for ‘ Superman.’”

In the technical categories, Matthew Libatique nabbed the cinematography prize for his work on “Black Swan,” and Guy Hendrix Dyas won for his production design on Christopher Nolan’s “Inception.”

In addition to the director winners, LAFCA presented two winners in music/score. Alexandre Desplat earned recognition for his score in “The Ghost Writer” along with Reznor and Ross.

Although their wins were limited, “Black Swan” and “Ghost Writer” had significant support throughout the voting.

Among the presumed Oscar contenders, there were few votes for “The Fighter,” “127 Hours,” “The Kids Are All Right” and “Another Year” in any categories. Christian Bale (“The Fighter”), James Franco (“127 Hours”) and Annette Bening (“The Kids Are All Right”) all received a handful of votes in the acting categories but were never much of a factor. Melissa Leo and Amy Adams did receive backing for supporting actress but wound up splitting “The Fighter’s” votes in that category. The Coen brothers’ “True Grit” had several passionate supporters but not enough votes to be a factor.

The L.A. critics group doesn’t see itself as a predictor or advocate for the Academy Awards and often goes its own way in choosing which films it honors.

The 36th annual Los Angeles Film Critics Assn. awards will be held Jan. 15, with special recognition for Paul Mazursky, who will receive the career achievement award.

nicole.sperling@latimes.com

Freelance writer Glenn Whipp contributed to this story.