does Ed25519 as used in Monero inherit the arithmetic capabilities that are possible with Schnorr signatures?

yes, Ed25519 can do Schnorr sigs if that's what you're asking

ed25519 is an elliptic curve, it does not inherit anything. If your question is 'can Schnorr signatures be implemented in ed25519', then yes.

right, I should have said EdDSA, not Ed25519. so the current signature scheme's capabilities in terms of stuff like adding up two public keys into a new one (which is possible with Schnorr)

can you restate the question? I don't follow

sure. the Schnorr signature algorithm allows for certain arithmetic combination of multiple public keys or signatures. I was made aware of this by Andrew Poelstra's work on scriptless scripts (github.com/BlockstreamResearch/scri…ripts/blob/master/md/atomic-swap.md). as the name implies, it's a method of employing more complex logic without new opcodes. since EdDSA is a variant of the Schnorr sig algo, I wondered if

this feature carries over to EdDSA, and thus Monero. if it does, it's one avenue by which an L2 can be constructed without adding scripting.

yep, it carries over to eddsa