### 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: Enumerative 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.

## Applications of the Schubert Calculus

Ok, this is going to be my last post in enumerative geometry for a while, as I’m kind of drifting away from the subject. However, this one will be fun. We’ve already established the structure of the cohomology ring for … Continue reading

## Pieri and Giambelli Formulas

It’s been a few weeks, but now I’m back and today we’ll talk about the multiplication in the cohomology ring of Grassmannians. Though we won’t talk about the Littlewood-Richardson rule in its full glory, we will howver discuss the special … Continue reading

## Schubert Classes and Cellular Cohomology

So, as of the last post in the series, we defined Schubert cells. We’re going to use them to discuss the Cohomology of the Grassmannian, and to write down an explicit basis. With an eye looking forward, next time, we’ll … Continue reading

## Schubert Varieties

It’s been awhile since the last post, but Spring Break happened. Anyway, back to Schubert Calculus! Last time, we discussed Grassmannians, this time, we’re going to talk about their most important subvarieties, the Schubert Varieties.

## Grassmannians, Redux

Ok, today we start our march towards Schubert Calculus. Before we start, we’ll review the Grassmannian variety itself, because it’s central to the story. A lot of this will consist of setting up notation, and there will be two different … Continue reading

## The Clemens Conjecture

This is a draft of a talk I’m giving on Thursday, mostly going over the work of Katz in this paper. Let’s begin with an informal statement of the conjecture: Conjecture: For every positive integer , a general quintic hypersurface … Continue reading