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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).
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https://hal.inria.fr/hal-02912057
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Elena Angelini, Cristiano Bocci, Luca Chiantini. CATALECTICANT INTERSECTIONS AND CONFINEMENT OF DECOMPOSITIONS OF FORMS. MEGA 2019 - International Conference on Effective Methods in Algebraic Geometry, Jun 2019, Madrid, Spain. ⟨hal-02912057⟩

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