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arXiv · 1704.02111

K\"ahler differential algebras for 0-dimensional schemes

Martin Kreuzer·Tran N. K. Linh·Le Ngoc Long
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Abstract

Given a 0-dimensional scheme in a projective space $\mathbb{P}^n$ over a field $K$, we study the K\"ahler differential algebra $\Omega_{R/K}$ of its homogeneous coordinate ring $R$. Using explicit presentations of the modules $\Omega^m_{R/K}$ of K\"ahler differential $m$-forms, we determine many values of their Hilbert functions explicitly and bound their Hilbert polynomials and regularity indices. Detailed results are obtained for subschemes of $\mathbb{P}^1$, fat point schemes, and subschemes of $\mathbb{P}^2$ supported on a conic.

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Martin Kreuzer, Tran N. K. Linh, Le Ngoc Long. 2017-04-07. K\"ahler differential algebras for 0-dimensional schemes. https://arxiv.org/abs/1704.02111

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