In his soliloquy, what are Hamlet's reasons for objecting to his mother re-marriage?
I'm assuming that you are talking about the soliloquy from Act I, Scene 2.
In this solioloquy, Hamlet objects to his mother's remarriage for three reasons.
The first reason he objects is because he feels she has remarried too soon after his father died. He talks about how the shoes she wore to follow his father to his grave are still new, but yet she's already remarried.
The second reason he objects is because he feels it's wrong that she married her husband's brother. He says that their marriage is incestuous and therefore wrong.
The last one seems to be that he doesn't think his uncle is as good as his father was. He talks about how they were as different as Hamlet is from Hercules. So it's sort of like he thinks his uncle isn't good enough for his mother.