UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

October 20, 2009

939 Evans Hall

3:45PM: Tangential schemes of determinantal varieties

Gregory G. Smith

The n-th jet scheme of a variety is a scheme that encodes the n-th order Taylor expansions of functions on the variety. The jet schemes associated to the varieties of matrices of a given rank are cut out by a relatively simple and explicit collection of polynomials. In this talk, I will survey the geometric properties of these jet schemes. I will also describe the minimal free resolution for the coordinate ring of the jet schemes of the variety of singular matrices.

5:00PM: Explicit moduli spaces for low degree covers

Melanie Matchett Wood

Location: Evans 939

Explicit moduli spaces for low degree covers of a scheme S have important arithmetic applications in the case S=Spec Z, in which case the covers include orders in low degree number fields. We will discuss how these spaces and also explicit moduli spaces for line bundles on low degree covers can be constructed to work over any scheme, and how certain free resolutions help us understand the degenerate covers that appear in the moduli spaces.

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