|Project:||Exploring the K-theory Class of 3-dimensional Matrices of Rank Less Than One|
Will be updated soon, when I am done with the background material for my project.
Suppose you have an affine space C and a subspace W. Let I be the ideal with polynomials that are zero at all points of W. Let A(W)=C[X]/I. My mentor and I discussed sequences of the form 0-->F1-->F2-->F3-->...-->Fn-->C[X]-->A(W)-->0. We also discussed groups actions, and talked about making the above sequence respect a group action imposed on the modules. Dr. Buch gave me several problems and asked me to find a sequence in the form above, and to modify it to respect group actions.
I also gave my first presentation.
We discussed the background from last week in much more detail, with an empathsis on theory and why gradings work, as opposed to simply finding the necessary sequence. We worked out the examples from last week in detail, and examined the k-theory classes.