Powers of sums and their homological invariants

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:223

Article

Nguyen, Hop D.¹  Thanh Vu² 

[1] Vietnam Acad Sci & Technol, Inst Math, 18 Hoang Quoc Viet, Hanoi, Vietnam

[2] Hanoi Univ Sci & Technol, 1 Dai Co Viet, Hanoi, Vietnam

关键词: Powers of ideals;    Sum of ideals;    Depth;    Regularity;    Castelnuovo-Mumford regularity;    Linearity defect;   

DOI  :  10.1016/j.jpaa.2018.10.010

来源: Elsevier

【 摘 要 】

Let R and S be standard graded algebras over a field k, and I subset of R and J subset of S homogeneous ideals. Denote by P the sum of the extensions of I and J to R k S. We investigate several important homological invariants of powers of P based on the information about I and J, with focus on finding the exact formulas for these invariants. Our investigation exploits certain Tor vanishing property of natural inclusion maps between consecutive powers of I and J. As a consequence, we provide fairly complete information about the depth and regularity of powers of P given that R and S are polynomial rings and either char k = 0 or I and J are generated by monomials. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free