Regularity of Tor for weakly stable ideals

Abstract

It is proved that if I and J are weakly stable ideals in a polynomial ring R = k[x_1, . . ., x_n], with k a field, then the regularity of Tor^R_i (R/I, R/J) has the expected upper bound. We also give a bound for the regularity of Ext^i_R (R/I, R) for I a weakly stable ideal.

Keywords

• Castelnuovo-Mumford regularity
• weakly stable ideals
• Tor
• Ext