What is the main conflict in The Big Sleep by Raymond Chandler?

The Big Sleep opens with private investigator Philip Marlowe visiting General Sternwood's mansion. Marlowe muses on the house's art and the fact that the furniture looks as if no one uses it. He first meets Carmen Sternwood, a flirt who, at twenty years old, is the younger of the General's two daughters. Then he meets the General, who receives him in his hothouse, a jungle-like setting in which the old man grows tropical orchids. The General tells Marlowe he is being blackmailed by someone named Arthur Gwynn Geiger, who wants the General to pay for Carmen's alleged gambling debts. Marlowe agrees to visit Geiger and put an end to the General's troubles.