Diagonal Subalgebras of Residual Intersections

2019/01/15 by H. Ananthnarayan, Neeraj Kumar, Ananthnarayan, H. +3
Computer Science · Mathematics · #13C40 #13D02 #13H10 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1901.05027

openalex publication_date 2019/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \sf k be a field, S be a bigraded \sf k-algebra, and S_Δ denote the diagonal subalgebra of S corresponding to Δ= \ (cs,es) | s ∈ ℤ \. It is know that the S_Δ is Koszul for c,e ≫ 0. In this article, we find bounds for c,e for S_Δ to be Koszul, when S is a geometric residual intersection. Furthermore, we also study the Cohen-Macaulay property of these algebras. Finally, as an application, we look at classes of linearly presented perfect ideals of height two in a polynomial ring, show that all their powers have a linear resolution, and study the Koszul, and Cohen-Macaulay property of the diagonal subalgebras of their Rees algebras.

Related

• Cohen-Macaulay residual intersections and their Castelnuovo-Mumford\n Regularity
• Subalgebras of bigraded Koszul algebras
• Koszul property of diagonal subalgebras
• Residual Intersections and Linear Powers
• Almost Complete Intersections: Regularity of powers and Rees algebra