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Does anybody know a good reference where the invariants for plane quartic curves are developed?

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Did you check "Polar Covariants of Plane Cubics and Quartics" by Dolgachev and Kanev?

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Ha! I had forgotten that paper, it is sure a good starting point. I'll take a look straight away, thank you. –  IMeasy Aug 19 '12 at 9:00
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