Finally, the eldest brother Sigdis was trapped in the Southmost portion of Skyrim, and cunningly challenged Lord Geirmund to a duel that the archmage could not refuse. The two proved to be even in might, and slew each other at the end of the battle near Ivarstead. The High King of the time had Geirmund entombed on an island in the lake now known as Geirmund Lake, and Sigdis was sealed there to be guarded by the archmage in death as he was slain in life.
Last of all, Gauldur was entombed in Reachwater Rock, close to where he had once lived. The High King, Harald, declared that Gauldur and his sons were to be forgotten, removed from all of history under pain of death. This was intended to keep the amulet from ever coming to light again and thus avoid the power and powerlust it created and inspired.
According to the notes, this happened four thousand years ago and the tombs are still sealed. Daynas was apparently lured mystically by the amulet somehow, and became somewhat crazed with desire for the artifact.
This leaves it to you to unearth and reunite the three pieces of Gauldur's amulet.
Now in possession of the Ivory Dragon Claw, you can operate the keyhole that Daynas is slumped against and cross the bridge it lets down.
The room here is small and circular, part of a series of entombment chambers. As you enter- or after slaying the two draugr who charged you across the bridge- look to the right first, where another draugr waits in a creche for you to call attention to yourself so that it can attack you. Slay it quickly- preferably from a distance- then look the other way.
The hall to the left (coming from the bridge) is trapped with a pair of spears, but the floor-panel is obvious and easily avoided. The end of the short hall contains a potion and a trapped chest. The chest is linked to a series of poison dart launchers, but these can be avoided by standing atop the chest as you open it to take its contents.