### 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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# Category Archives: Examples

## Constructing Nodal Curves

So, I don’t really have a full length post in me at the moment. However, here’s a nice trick that I’ve learned recently, plus some motivation. With this, it’s easy to write down explicitly a curve of arbitrary degree in … Continue reading

Posted in Algebraic Geometry, Curves, Examples
11 Comments

## Group Schemes and Moduli (I)

Hi! My name is Matt DeLand, I’m a graduate student at Columbia and I’m responding to Charles’ call for cobloggers. I also study Algebraic Geometry, and have been enjoying Charles’ posts; hopefully I can help out and make some positive … Continue reading

Posted in AG From the Beginning, Algebraic Geometry, Examples
5 Comments

## Canonical Linear Systems

Given any curve , we have a natural linear system , consisting of all the effective canonical divisors. Now, sometimes this is unhelpful. After all, if , then the canonical system has negative degree, so . If , then the … Continue reading

Posted in AG From the Beginning, Algebraic Geometry, Curves, Examples
5 Comments

## Examples of Moduli Spaces

Now we’re done constructing , so it’s time to get the general Hilbert scheme done, and then to construct some other moduli spaces. Now, as , we can see that is a subfunctor of , so we want to try … Continue reading

## The Hilbert Scheme

Now that we have a notion of moduli space, we’re going to look at several concrete examples. I mentioned that the Grassmannian is a fine moduli space for -planes in . We’ll make use of this to construct several more. … Continue reading

## Grassmannians and Flag Varieties

Back in the second post, we defined projective space to be the collection of lines through the origin in affine space. A natural generalization is to look at -planes through the origin in affine space. At first glance, we might … Continue reading

Posted in AG From the Beginning, Algebraic Geometry, Examples
4 Comments

## The Segre Embedding

Today, we talk about the Segre Embedding. This will let us say a bit more about the products of varieties that were mentioned before.

Posted in AG From the Beginning, Algebraic Geometry, Examples
9 Comments