Castelnuovo–Mumford Regularity of Sums of Powers of Polynomial Ideals

Abstract

The asymptotic behavior of the Castelnuovo–Mumford regularity of sums of powers of polynomial ideals is studied. It is shown that as well as are bounded by linear functions of n provided dim S/(I + I ₁ +···+ I _p ) ≤ 1. When I ₁,…, I _p are monomial ideals such that dim S/(I ₁ +···+ I _p ) = 0, we also show that is not necessarily an asymptotically linear function of n, but the limit always exists.

Key Words:

• Castelnuovo–Mumford regularity
• Newton polytope
• Power of ideals

2000 Mathematics Subject Classification:

• 13D45
• 13P10

ACKNOWLEDGMENTS

The authors were supported in part by the National Basic Research Program (Vietnam).

Notes

Communicated by I. Swanson.