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 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).

Angelini, E., Bocci, C., Chiantini, L. (2022). Catalecticant intersection and confinement of decompositions of forms. JOURNAL OF SYMBOLIC COMPUTATION, 109, 220-237 [10.1016/j.jsc.2020.07.003].

Catalecticant intersection and confinement of decompositions of forms

Angelini E.;Bocci C.;Chiantini L.
2022-01-01

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 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).
Angelini, E., Bocci, C., Chiantini, L. (2022). Catalecticant intersection and confinement of decompositions of forms. JOURNAL OF SYMBOLIC COMPUTATION, 109, 220-237 [10.1016/j.jsc.2020.07.003].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1167685