The curse is significant because it highlights Oedipus' tragic fate and the complexities of his character. Oedipus is portrayed as a noble and virtuous man, yet his actions are driven by hubris (excessive pride) and a lack of self-awareness. By cursing the murderer, he unknowingly seals his own doom.
The irony deepens when Oedipus eventually discovers the truth about his past and realizes that he has fulfilled the prophecy he was trying to avoid. He curses the murderer not knowing it is himself, emphasizing the tragic nature of his downfall and the inescapable consequences of his actions.
The play explores themes of fate, free will, and the tragic consequences of human error, making Oedipus' curse on the murderer a poignant moment of self-realization and dramatic irony.