On the Regularity of Codimension Two Surfaces and Threefolds with Singular Loci

ABSTRACT

For projective codimension two surfaces and threefolds whose singular locus is one dimensional, we get the sharp Castelnuovo–Mumford regularity bound in terms of degrees of defining equations and give the classification of nearly extremal cases. This is a generalization of the result of Bertram et al.

Key Words:

• Castelnuovo–Mumford regularity
• Codimension two singular varieties
• Defining equations
• Liaison

Mathematics Subject Classifications (2000):

• 14M07
• 14N05
• 14J30

ACKNOWLEDGMENTS

It is our pleasure to thank Prof. Seunghun Lee for informing us about Lemma 2.6. The first author was supported in part by KRF (grant No.KRF-2002-070-C00003). The second author was supported in part by KOSEF(grant No. R01-2002-000-00151-0).

Notes

^#Communicated by I. Swanson.