Meaning of dialogue about "Paul Giamatti" said by Jeff Winger in Community

The Ark of the Covenant in Raiders of the Lost Ark would kill you if you looked at it.

Jeff wants Abed to close his eyes. Abed is an extreme movie fan who often can only be related to in the context of pop culture movies. So the best way to get Abed to close his eyes is to relate the act to a popular movie. Jeff chooses Raiders of the Lost Ark, a popular movie in which if you looked at the Ark when it was open it would kill you. Abed can relate and closes his eyes.

Paul Giamatti is the physical opposite of Alison Brie.

Everyone always cuts Annie a break because she is a very pretty young woman. Jeff wants to strip that away and make them look not at her appearance, but at what she did. To overcome the cuteness, he has them close their eyes and picture her as Paul Giamatti--an extremely non-cute (many would say outright unattractive) actor. Picturing her as Paul Giamatti allows them to see through her cuteness to the fact that what she did was bad (at least for the group; arguably, getting Chang fired was a good thing to do since he was a lousy teacher).

As explained here:

She naturally turns Chang in and he’s replaced by a real Spanish teacher, and now the whole class is in trouble. Jeff flips out on Annie for it (after a nice sequence in which everyone’s groans is can’t disguise Annie’s happy sigh), and convinces the whole group not to give in to her young cuteness (“Picture her as Paul Giamatti!”).