Waring decompositions of the product of two quadrics: the small rank cases
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912735322701824 |
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| author | Bhat, Meghana Carlini, Enrico Dubey, Saipriya Masuti, Shreedevi K. |
| author_facet | Bhat, Meghana Carlini, Enrico Dubey, Saipriya Masuti, Shreedevi K. |
| contents | In this paper we study forms of the type $(x_1^2+ \cdots +x_m^2)(y_1^2+ \cdots+y_n^2)$ using projections. For $m=1, m=2$, and for any $n$ we describe: the forbidden locus, the structure and the Hilbert function of all minimal apolar sets. In particular, we show that every minimal apolar ideal has the same Hilbert function. For $m,n \geq 3,$ we provide new lower and upper bounds for the Waring rank. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_23035 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Waring decompositions of the product of two quadrics: the small rank cases Bhat, Meghana Carlini, Enrico Dubey, Saipriya Masuti, Shreedevi K. Commutative Algebra Algebraic Geometry Primary:14N07, Secondary:13D40 In this paper we study forms of the type $(x_1^2+ \cdots +x_m^2)(y_1^2+ \cdots+y_n^2)$ using projections. For $m=1, m=2$, and for any $n$ we describe: the forbidden locus, the structure and the Hilbert function of all minimal apolar sets. In particular, we show that every minimal apolar ideal has the same Hilbert function. For $m,n \geq 3,$ we provide new lower and upper bounds for the Waring rank. |
| title | Waring decompositions of the product of two quadrics: the small rank cases |
| topic | Commutative Algebra Algebraic Geometry Primary:14N07, Secondary:13D40 |
| url | https://arxiv.org/abs/2511.23035 |