At the time of writing, the general problem of finding the maximum Waring rank for homogeneous polynomials of a fixed degree and in a fixed number of variables (or, equivalently, the maximum symmetric rank for symmetric tensors of a fixed order and in a fixed dimension) is still unsolved. To our knowledge, the answer for ternary quartics is not widely known and can only be found among the results of a master's thesis by Johannes Kleppe at the University of Oslo (1999). In the present work we give a (direct) proof that the maximum rank for plane quartics is seven, following the elementary geometric idea of splitting power sum decompositions along three suitable lines.
A proof that the maximum rank for ternary quartics is seven
DE PARIS, ALESSANDRO
2015-01-01
Abstract
At the time of writing, the general problem of finding the maximum Waring rank for homogeneous polynomials of a fixed degree and in a fixed number of variables (or, equivalently, the maximum symmetric rank for symmetric tensors of a fixed order and in a fixed dimension) is still unsolved. To our knowledge, the answer for ternary quartics is not widely known and can only be found among the results of a master's thesis by Johannes Kleppe at the University of Oslo (1999). In the present work we give a (direct) proof that the maximum rank for plane quartics is seven, following the elementary geometric idea of splitting power sum decompositions along three suitable lines.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
