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The Waring loci of ternary quartics. (English) Zbl 1061.14057
Summary: Let \(s\) be any integer between 1 and 5. We determine necessary and sufficient conditions that a ternary quartic be expressible as a (possibly degenerate) sum of fourth powers of \(s\) linear forms.

MSC:
14N05 Projective techniques in algebraic geometry
14L35 Classical groups (algebro-geometric aspects)
13A50 Actions of groups on commutative rings; invariant theory
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
11E76 Forms of degree higher than two
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