If I cast Genesis Wave and one of the cards that I reveal with it is an Aura, I can put it on the battlefield, but can I attach it to a (legal) target?
Yes, you can attach a revealed aura to a legal object/player, in fact, you must do so if possible (if you choose to put the aura out). If you can't, the aura stays in the library, and is then put into the graveyard along with the other revealed cards you didn't put on the field. Be aware, that you cannot attach the aura to something that would enter the battlefield along with it.
It's worth noting that attaching an Aura to something this way doesn't target anything. (Auras only have targets while they are spells on the stack.) If an effect causes you to put an Aura directly onto the battlefield, you just choose something for it to enter attached to. So you could even attach the Aura to a creature with shroud, or an opponent's creature with hexproof, if you want.
Also, since all of the permanents entering from Genesis Wave enter at the same time, you cannot choose to attach the aura to something else entering from G-wave. It has to be something already on the battlefield.
(Contrast with Primal Surge, which puts permanents into play one at a time.)
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(Contrast with Primal Surge, which puts permanents into play one at a time.)
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