Wronskians form the inverse system of the arcs of a double point
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910448025075712 |
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| author | Manssour, Rida Ait El Pogudin, Gleb |
| author_facet | Manssour, Rida Ait El Pogudin, Gleb |
| contents | The ideal of the arc scheme of a double point or, equivalently, the differential ideal generated by the ideal of a double point is a primary ideal in an infinite-dimensional polynomial ring supported at the origin. This ideal has a rich combinatorial structure connecting it to singularity theory, partition identities, representation theory, and differential algebra. Macaulay inverse system is a powerful tool for studying the structure of primary ideals which describes an ideal in terms of certain linear differential operators. In the present paper, we show that the inverse system of the ideal of the arc scheme of a double point is precisely a vector space spanned by all the Wronskians of the variables and their formal derivatives. We then apply this characterization to extend our recent result on Poincaré-type series for such ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08964 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wronskians form the inverse system of the arcs of a double point Manssour, Rida Ait El Pogudin, Gleb Commutative Algebra Symbolic Computation Algebraic Geometry Combinatorics 12H05, 13D40, 05A17 The ideal of the arc scheme of a double point or, equivalently, the differential ideal generated by the ideal of a double point is a primary ideal in an infinite-dimensional polynomial ring supported at the origin. This ideal has a rich combinatorial structure connecting it to singularity theory, partition identities, representation theory, and differential algebra. Macaulay inverse system is a powerful tool for studying the structure of primary ideals which describes an ideal in terms of certain linear differential operators. In the present paper, we show that the inverse system of the ideal of the arc scheme of a double point is precisely a vector space spanned by all the Wronskians of the variables and their formal derivatives. We then apply this characterization to extend our recent result on Poincaré-type series for such ideals. |
| title | Wronskians form the inverse system of the arcs of a double point |
| topic | Commutative Algebra Symbolic Computation Algebraic Geometry Combinatorics 12H05, 13D40, 05A17 |
| url | https://arxiv.org/abs/2405.08964 |