The ambiguity in the character of Joe Christmas is particularly interesting, in my opinion. Christmas drives a considerable amount of the action in the story, and in his turn he is driven by a profound irritation that stems from doubts about his heritage. He is:
"Doomed in motion, driven by the courage of flagged and spurred despair..."
His despair grows from the fact that he believes he will never know "who he is".
Examining the function of ambiguity in his character should be very interesting and plenty of scholarship has been done in this area and is available for research. Some questions you might be asking are:
- How does Joe Christmas develop an "absolute" or "absolutist" attitude in response to the ambiguity that plagues him?
- What does this "absolute" attitude lead to - strength, weakness, violence...? How exactly does it lead where it does?
- How does the ambiguity surrounding Joe Christmas contrast with the naive (yet successful) self-assurance of Lena?
- How does the ambiguity of Christmas relate to the larger themes, situations, and characters of the novel?
Another idea for a term paper on this novel might be to explore the concept of fatherlessness. This idea relates significantly to Joe Christmas, but also to the pregnant character, Lena. This idea can be connected to the treatment of religion in the novel as well, specifically connecting to ideas of a Christian God as a stern, distant, and supremely judgemental father figure who shapes the lives of his "children".
The role that religion plays in the novel is also very interesting. Religion and social judgement are tightly connected in the examples of several characters, including Christmas, Eupheus Hines, Joe's father McEachern, and Hightower. A paper exploring religion in the novel might take up questions of how religion shapes characters in terms of their fates, judgements, fixations and personalities.
The eNotes page on themes from this novel identifies "Destructive Righteousness" as a theme, which nicely sums up one way religion functions in the novel. An examination of the novel's religious symbolism could also be included in a paper on this topic.
The best advice will ultimately lead you to choose an aspect of the novel that excites or interests you. A rich novel like this one offers many options for a term paper assignment, but the best one for you will be one that lets you examine the characters and themes you find most compelling.