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arXiv · 2508.00196

The Canonical Exact Sequence of Differential Modules for 0-Dimensional Schemes

Tran N. K. Linh·Le Ngoc Long
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Abstract

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 K\"ahler differential module. We also provide a formula for the Hilbert polynomial of K\"ahler differential modules when $\X$ is either a fat point scheme or a 0-dimensional locally monomial Gorenstein scheme.

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Tran N. K. Linh, Le Ngoc Long. 2025-07-31. The Canonical Exact Sequence of Differential Modules for 0-Dimensional Schemes. https://doi.org/10.2140/pjm.2026.344.47

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