at - to

[dilodi83]

- what time did Nygel finally turn up at/to the party, then?

the book where I've taken this sentence from says that only at is correct, but I cannot understand why to is incorrect.
If "turn up" in this sentence means "to go to", and it indicates a movement, why to write at, which does not indicate any sort of movement?
Or does "to turn up" follow the rule like "to arrive at" and it needs to be followed by at?
Could you explain this, please?

[bhaisahab]

- what time did Nygel finally turn up at/to the party, then?

the book where I've taken this sentence from says that only at is correct, but I cannot understand why to is incorrect.
If "turn up" in this sentence means "to go to", and it indicates a movement, why to write at, which does not indicate any sort of movement?
Or does "to turn up" follow the rule like "to arrive at" and it needs to be followed by at?
Could you explain this, please?

To "turn up" somewhere is to arrive there, not go there. We arrive at places, not to.