About this blog
Rigorous trivialities is a web log about mathematics, but especially geometry, broadly construed. Contributors will be Charles Siegel, Jim Stankewicz and occasionally Matt Deland. Charles specializes in algebraic geometry, topology and mathematical physics. Jim specializes in arithmetic algebraic geometry. Matt has transitioned from algebraic geometry to work in industry.
Header is taken from the larger work by fdecomite under the creative commons license.
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Monthly Archives: November 2010
Prym Varieties
Let be an unramified double cover, where is geneus . Then has genus by the Riemann-Hurwitz formula. Now, encodes lots of information about the geometry of , especially with the additional data of the theta divisor. It turns out that … Continue reading
Rational Normal Scrolls
Today, we’re going to talk about a very important class of rational varieties, that show up all the time, in quite a variety of different contexts, and at the end, we’ll talk about why.
Determinantal Varieties
Let be the projectivization of . Then for all , we have a variety given as the set of matrices of rank at most , which is given by the vanishing of the determinents of minors. We call these the … Continue reading
Technology Survey!
I know I still have a few readers out there, and some of you are probably technophiles, so here’s a question: I’ve been considering switching from live-texing of things to a digital pen of some sort. Anyone have any experience … Continue reading
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Low Genus Moduli of Curves
Pretty much everything in this post is in Mumford’s “Curves and their Jacobians,” but I do a couple of things slightly differently, and I intend to supply a bit more detail in some places. The goal here is to construct … Continue reading
The Stanley-Reisner Ring
Today, we’re going to do something completely different, but which most of my peers seem not to have seen, but is a very cool application of algebraic geometry.
A short post on bitangents
Today’s post will be, as the title says, a bit short. It will, more-or-less finish our current discussion of theta characteristics, and then we’ll get back to something else. But we’ll derive a nice case of a classical formula.
Theta Characteristics and Quadrics in Characteristic Two
Last time we defined theta characteristics as square roots of the canonical bundle. Today, we’re going to analyze the notion a bit, and relate them to quadrics in characteristic two.
Subvarieties of Jacobians
For this whole post, we’ll take to be a curve and the Jacobian of the curve. We’re going to construct several special subvarieties (not special in any technical sense, though) of , which encode a great deal of geometric information … Continue reading
Jacobians of Curves
As promised in the last post, I’m making another go at MaBloWriMo…maybe others will as well. I don’t know if I’m going to have a coherent topic over the course of this month, but I’ll be starting with abelian varieties … Continue reading
Rigorous Trivialities 