The Canonical Exact Sequence of Differential Modules for 0-Dimensional Schemes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908475069562880 |
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| author | Linh, Tran N. K. Long, Le Ngoc |
| author_facet | Linh, Tran N. K. Long, Le Ngoc |
| contents | Given a 0-dimensional scheme $\X$ in $\mathbb{P}^n_K$ over a perfect field $K$, we examine the second differential power of its homogeneous vanishing ideal. This enables us to establish the canonical exact sequence for the associated Kähler differential module. We also provide a formula for the Hilbert polynomial of Kähler differential modules when $\X$ is either a fat point scheme or a 0-dimensional locally monomial Gorenstein scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00196 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Canonical Exact Sequence of Differential Modules for 0-Dimensional Schemes Linh, Tran N. K. Long, Le Ngoc Algebraic Geometry Commutative Algebra Given a 0-dimensional scheme $\X$ in $\mathbb{P}^n_K$ over a perfect field $K$, we examine the second differential power of its homogeneous vanishing ideal. This enables us to establish the canonical exact sequence for the associated Kähler differential module. We also provide a formula for the Hilbert polynomial of Kähler differential modules when $\X$ is either a fat point scheme or a 0-dimensional locally monomial Gorenstein scheme. |
| title | The Canonical Exact Sequence of Differential Modules for 0-Dimensional Schemes |
| topic | Algebraic Geometry Commutative Algebra |
| url | https://arxiv.org/abs/2508.00196 |