Checkpointing in a deferred update database

Something that I just cannot get my head around.

Checkpointing writes all dirty pages from ram memory to disk. For Deferred update systems, data changes recorded in the log file are applied to the database on commit.

In a deferred update system, a transaction is executing when a checkpoint occurs, all dirty pages are written to disk. If the system crashes prior to the transaction committing, should the recovery manager not undo the effect of the transaction on disk. (disk updates by Checkpoing not log file).

Really appreciate any help with this.