Title:

On the splitting of the 2nd exterior power of the conormal module from Tor.

Abstract:

Let R be a local Noetherian ring and I an ideal of R generated by n \geq 2 elements. In “The Syzygies of the Conormal Module,” Simis and Vasconcelos give an embedding map, and a somewhat cryptic remark that this map causes a splitting of the 2nd exterior power of the conormal module from Tor_1(I,R/I). In this talk we utilize differential graded algebra resolutions to define an explicit splitting map and show that if I/I^2 is free (or has enough free summands), then the 2nd exterior power of the conormal module (or its free summands) will split from Tor_1(I,R/I).