“Veteran New York City Ballet fans — who witnessed the glory days under Balanchine — habitually carp about Peter Martins’s ballets. Even these naysayers admit he has craft, but they sense the absence of imagination. They’re also put off by the aridity of his pieces in the classical mode and the hostility between the sexes that prevails in his contemporary-style works. It’s possible, too, that the detractors conflate Martins’s lack of choreographic genius with other perceived flaws. During his tenure, the custodianship of the Balanchine repertoire has, arguably, been careless.”