Free resolutions and Castelnuovo-Mumford regularity.

Nic Clarke

Frank Adams 1,

One way to study graded modules it to try and compute the (minimal) graded free resolution and associated invariants. Hilbert's syzygy theorem states that over a polynomial ring the resolution is always finite. In this case we can compute the Castelnuovo-Mumford regularity by looking at the graded Betti numbers. The regularity gives bounds on the generators and relations of the module as well as all the higher syzygys. In the talk I will show how to construct free resolutions via examples and explain how we compute the regularity in some easy cases. If there is time I will show how we can relate some of this to the underlying algebraic geometry

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