Grassmann cactus variety and socle dimension
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866911441659887616 |
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| author | Buczyńska, Weronika Buczyński, Jarosław Gałązka, Maciej |
| author_facet | Buczyńska, Weronika Buczyński, Jarosław Gałązka, Maciej |
| contents | Grassmann cactus variety is a common generalisation of Grassmann secant variety and cactus variety. In their definitions one considers the vector spaces of fixed dimension that are contained in the linear span of some finite schemes. We prove that to characterise Grassmann cactus varieties it is enough to use finite schemes that locally have low socle dimension. This motivates the study of parameter spaces of such schemes and simplifies calculations of examples of Grassmann cactus varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21586 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Grassmann cactus variety and socle dimension Buczyńska, Weronika Buczyński, Jarosław Gałązka, Maciej Algebraic Geometry 14A15 (Primary) 13H10, 14D99, 14N07 (Secondary) Grassmann cactus variety is a common generalisation of Grassmann secant variety and cactus variety. In their definitions one considers the vector spaces of fixed dimension that are contained in the linear span of some finite schemes. We prove that to characterise Grassmann cactus varieties it is enough to use finite schemes that locally have low socle dimension. This motivates the study of parameter spaces of such schemes and simplifies calculations of examples of Grassmann cactus varieties. |
| title | Grassmann cactus variety and socle dimension |
| topic | Algebraic Geometry 14A15 (Primary) 13H10, 14D99, 14N07 (Secondary) |
| url | https://arxiv.org/abs/2507.21586 |