On the regularity of product of pure power complete intersections

TL;DR

This paper investigates the regularity of products of pure power complete intersections, establishing an upper bound for the regularity of their product based on individual regularities.

Contribution

It proves that the regularity of the product of three pure power complete intersections does not exceed the sum of their individual regularities.

Findings

Reg(I^n) can be computed using induction.

reg(IJK) ≤ reg(I) + reg(J) + reg(K).

Provides bounds for regularity of product of complete intersections.

Abstract

Let I be a complete intersection in a polynomial ring over a field, the Castelnuovo-Mumford regularity of I^n is given by using an induction method. When I, J and K are three pure power complete intersections, it is proved that reg(IJK) is not more than reg(I)+reg(J)+reg(K).