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

2025/07/31 by Linh, Tran N. K., Long, Le Ngoc
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.00196

Abstract

Given a 0-dimensional scheme \X in ℙⁿ_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.

Citations

• Differential theory of zero-dimensional schemes
• Kähler differential algebras for 0-dimensional schemes
• Symbolic powers of ideals

Related

• Differential theory of zero-dimensional schemes
• Kähler differential algebras for 0-dimensional schemes
• Hilbert Polynomials of Kähler Differential Modules for Fat Point Schemes
• Solving differential equations
• DG module structures and minimal free resolutions modulo an exact zero-divisor