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This paper exhibits some new examples of the behavior of theCastelnuovo-Mumford regularity of homogeneous ideals in polynomial rings. Moreprecisely, we present new examples of homogenous ideals with large regularitycompared to the generating degree. Then we consider the regularity jumps ofideals. In particular we provide an infinite family of ideals having regularityjumps at a certain power.

Some Remarks on Ideals with large Regularity and Regularity Jumps