Abstract
A plane quartic curve is called Lüroth if it contains the ten vertices of a complete pentalateral. White and Miller constructed in 1909 a covariant quartic fourfold, associated to any plane quartic. We review their construction and we show how it gives a computational tool to detect if a plane quartic is Lüroth. As a byproduct, we show that the 28 bitangents of a general plane quartic correspond to 28 singular points of the associated White–Miller quartic fourfold.
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