A remark on Waring decompositions of some special plane quartics
Abstract
This work concerns Waring decompositions of a certain kind of plane quartics of high rank. The main result is the following. Let x, l1, ...., l7 be linear forms and q a quadratic form on a vector space of dimension 3. If x2q=l14+...+l74 and the lines l1=0, ..., l7=0 in P2 intersect x=0 in seven distinct points, then the line x=0 is (possibly improperly) tangent to the conic q=0.
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