On the core and adjoint of the product of complete ideals in two-dimensional regular local rings

2025/06/17 by Clare D’Cruz, D'Cruz, Clare, Saipriya Dubey +3
Mathematics · #Advanced Topics in Algebra #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2506.14228

openalex publication_date 2025/06/17 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

Using joint reductions of complete ideals, we find expressions for the core and adjoints of the product of complete ideals in a two-dimensional regular local ring. We also compute their colengths. Our results strengthen a generalization of the Briançon-Skoda theorem due to D. Rees and J. D. Sally.

Citations

• On conjectures of Itoh and of Lipman on the cohomology of normalized blow-ups
• A vanishing theorem for finitely supported ideals in regular local rings
• When does the subadditivity theorem for multiplier ideals hold?
• Adjoints of ideals in regular local rings
• Jacobian ideals and a theorem of Brian\c con-Skoda.

Related

• The core of a module and the adjoint of an ideal over a two dimensional\n regular local ring
• Core and residual intersections of ideals
• Local cohomology of multi-Rees algebras, Joint reduction numbers and product of complete ideals
• The structure of the core of ideals
• Adjoints of ideals in regular local rings