Almost Complete Intersections: Regularity of powers and Rees algebra

An almost complete intersection ideal can be seen as a $d$-sequence ideal with the minimal number of generators being one more than its height. In this paper, we give exact formulas for the regularity of powers of graded almost complete intersection ideals satisfying certain conditions. We also present the minimal bigraded free resolutions of Rees algebras associated with linear type ideals having one generator more than their grade and study the properties of Cohen-Macaulayness, Koszulness associated to their diagonals.