Catalecticant intersections and confinement of decompositions of forms. (March 2022)

• Record Type: Journal Article
• Authors: Angelini, Elena; Bocci, Cristiano; Chiantini, Luca
• Is Part Of: Journal of symbolic computation. Volume 109(2022)
• Page Start: 220
• Page End: 237
• Publication Date: 2022-03
• Subjects: 14N07 -- 14N05 -- 15A69 -- 14P05 -- 14Q99; Waring decomposition -- Unidentifiable case -- Elliptic curve -- Catalecticant map -- Real rank; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.07.003
• Languages: English
• ISSNs: 0747-7171

Abstract

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 (1890) 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).