Kähler differential algebras for 0-dimensional schemes

2017/04/07 by Martin Kreuzer, Kreuzer, Martin, Tran N. K. Linh +3 · 1 citation
Mathematics · #13D40 #13N05 #14N05 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13D40 #msc:13N05 #msc:14N05

paper · pdf · doi:10.48550/arxiv.1704.02111

arxiv created 2017/04/07 · arxiv updated 2017/04/10

Abstract

Given a 0-dimensional scheme in a projective space ℙⁿ over a field K, we study the Kähler differential algebra Ω_R/K of its homogeneous coordinate ring R. Using explicit presentations of the modules Ω^m_R/K of Kähler 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 ℙ¹, fat point schemes, and subschemes of ℙ² supported on a conic.

Cited by

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

Related

• Hilbert Polynomials of Kähler Differential Modules for Fat Point Schemes
• Differential theory of zero-dimensional schemes
• The Canonical Exact Sequence of Differential Modules for 0-Dimensional Schemes
• Kaehler differentials for fat point schemes in P¹xP¹
• The Kähler different of a 0-dimensional scheme