APRIL and May are among the busiest months in the performing-arts calendar. Tonight, the Academy Awards will be televised from Los Angeles; and after a flurry of theater openings in coming weeks, the Tony Awards will take place in June.
In the international film community, an ongoing dispute is percolating over the Academy of Motion Picture Arts and Sciences' rule about which films qualify for its best foreign-language film award. This year, academy voters eliminated the critically acclaimed ''Red'' from consideration, saying that Switzerland, which submitted it, could not claim the picture because the director, Krzysztof Kieslowski, is Polish, and the language spoken in it is French. (Kieslowski later picked up Oscar nominations as director and co-writer.)
Increasingly, critics of the academy say the qualifying rules need to change to accommodate international films whose origins are not clear-cut.
Last year, the rules were bent to include ''The Wedding Banquet,'' submitted by Taiwan but shot in New York with a partly American crew and a large amount of English dialogue. Two other nominees from last year, ''Farewell My Concubine'' (Hong Kong) and ''The Scent of Green Papaya'' (Vietnam), were made outside the countries that submitted them.
Major Bolshoi shakeups
Ballet fans are watching to see what emerges from the disarray that has plagued Moscow's Bolshoi Theatre. On Tuesday, 34-year veteran prima ballerina, Natalia Bessmertnova, quit after the company named the person to replace artistic director Yuri Grigorevich.
During his 30 years in that post, Grigorevich had ruled the company with a firm hand, and, according to ballet critics, did not bother to choreograph new works or improve the repertoire. What he did, however, was ingratiate himself with officials and a core of loyal dancers, to whom he gave the primary roles. Grigorevich resigned March 9 after feuding with the Bolshoi's general director, Vladimir Kokonin, over Kokonin's attempts to restructure contracts.
On March 10, ballerinas loyal to Grigorevich refused to take part in a production of ''Romeo and Juliet,'' and in response Kokonin suspended more than a dozen of them. Russian President Boris Yeltsin, who apparently did not like the idea of ballerinas out on strike, or the near collapse of this 219-year-old cultural institution, fired Kokonin.
The troubled company has named dancer Vladimir Vasyliev as its new artistic director. Vasyliev was forced out of the Bolshoi company several years ago, along with his wife, prima ballerina Yekaterina Maximova. Vasyliev told the Itar-Tass news agency: ''The Bolshoi's reputation today is musty and stained by strife and squabbles. Only artistic creativity will clear its reputation.''
A new Hamlet
English actor Ralph Fiennes, who played a death-camp commandant in ''Schindler's List'' and, more recently, an ethically challenged TV game-show contestant in ''Quiz Show,'' is heading toward Broadway with his version of ''Hamlet.''
Tickets have already gone on sale for the show, which starts previews on April 14 at the Belasco Theater in New York and is scheduled to run through July 22. This production of ''Hamlet'' is currently playing in London, and the critical response has been mixed.
American conductor for Paris Opera
James Conlon was appointed principal conductor of the Paris National Opera earlier this month, the first time an American-born maestro has held that post. He signs on as music adviser this year, but does not take over full-time until 1996. Conlon has built his career mostly in Europe, as music director of the city of Cologne, Germany, and conductor of the Cologne Opera. His appointment comes at a dicey time: Power struggles have disrupted the Paris Opera. Last summer, South Korean-born conductor Myung-Whun Chung was dismissed as music director, and his predecessor, Daniel Barenboim, was asked to leave after only a few months in 1989.
'Surtitles' at the Met
New York's Metropolitan Opera has settled on a device that will allow concertgoers to have instant translations of song texts. The company has long rejected the use of ''surtitles'' -- in which the translated verses are projected above the stage. But in a recent announcement, the opera said it will use individual screens on the backs of seats beginning next fall with Verdi's ''Otello.''