The Great Gatsby, men talking with curious intensity

Could you please tell me the meaning of "intensity" and "curious" in this excerpt from the chapter Three of The Great Gatsby?

I looked around. Most of the remaining women were now having fights with men said to be their husbands. Even Jordan’s party, the quartet from East Egg, were rent asunder by dissension. One of the men was talking with curious intensity to a young actress, and his wife after attempting to laugh at the situation in a dignified and indifferent way broke down entirely and resorted to flank attacks—at intervals she appeared suddenly at his side like an angry diamond and hissed “You promised!” into his ear.

Thank you.