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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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