CATALECTICANT INTERSECTIONS AND CONFINEMENT OF DECOMPOSITIONS OF FORMS
Abstract
We introduce the notion of confinement of decompositions for forms or vector of
forms. The confinement, when it holds, lowers the number of parameters that one needs to consider,
in order to find all the possible decompositions of a given set of data. With the technique
of confinement, we obtain here two results. First, we give a new, shorter proof of a result by
London ([21]) that 3 general plane cubics have 2 simultaneous Waring decompositions of rank
6. Then we compute, with the software Bertini, that 4 general plane quartics have 18 different
decompositions of rank 10 (a result which was not known before).
Origin : Files produced by the author(s)
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