In "The Lady with the Pet Dog" by chekhov, why are we given little information about the female antagonist?
You have asked an interesting question. On the one hand, I actually disagree with it, because I do feel we are given lots of information about Anna Sergeyevna in this excellent short story. However, on the other hand, I can understand from where this question emerges, as the point of view, third person limited, focuses on the character of Gurov, so we see into his thoughts, motives and feelings. Although Anna Sergeyevna therefore could be said to possess a less important place in the structure of the tale, I would disagree. Primarily, this story shows us the character development of Gurov from a casual and serial seducer to someone who has learnt some serious moral lessons about life and himself.
Note how when the story starts, we are told that he has become "constantly unfaithful" to his rather severe wife. He speaks slightingly of women, calling them "the lower race," and in the second section of the tale he is rather callously able to munch on some watermelon whilst Anna Sergeyevna cries desperately.
And yet, by the end of the tale, Gurov is transformed to a male who is much more self-aware and who has learned to respect Anna Sergeyevna and has identified the mutual, deep and abiding love they share:
He and Anna Sergeyevna loved one another as people who are very close and intimate, as husband and wife, as dear friends love one another. It seemed to them that fate had intended them for one another, and they could not understand why she should have a husband, and he a wife. They were like to migrating birds, the male and the female, who had been caught and put into separate cages. They forgave one another all that they were ashamed of in the past and in the present, and felt that this love of theirs had changed them both.
What a transformation! From regarding himself as free to be able to "play the field," Gurov recognises how actually he is "caged" and recognises how the love he has for Anna Sergeyevna has transformed him.
So, whilst in one sense you are right, we are not given much information about Anna Sergeyevna, from another perspective I think this story shows the moral awakening and development of Gurov, who starts off as a heartless cad and ends a more sensitive and self-aware individual.