### 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.

### Categories

- Abelian Varieties AG From the Beginning Algebraic Geometry Algebraic Topology Big Theorems Cohomology Combinatorics Complex Analysis Computational Methods Conferences Cranks Curves Deformation Theory Differential Geometry Enumerative Geometry Examples Group Theory Hilbert Scheme Hodge Theory ICTP Summer School Intersection Theory Knot Theory MaBloWriMo Math Culture Mathematical Physics Moduli of Curves Talks Toric Geometry Uncategorized Vector Bundles
### Recent Comments

### Links

### Math Blogs

- 0xDE
- 360
- A Mind for Madness
- A Neighborhood of Infinity
- A Singular Contiguity
- Aline’s Weblog
- Arcadian Functor
- Ars Mathematica
- Blog of a Math Teacher
- Casting out Nines
- Combinatorics and More
- Concrete Nonsense
- Disquisitiones Mathematicae
- Dung Hoang Nguyen’s Weblog
- E. Kowalski’s Blog
- eon
- EvolutionBlog
- Geometric Algebra
- God Plays Dice
- Good Math, Bad Math
- gyre & gimble
- Halfway There
- Hydrobates
- in Theory
- Intrinsically Knotted
- Let’s Play Math
- Low Dimensional Topology
- Mathematics and Physics
- Mathematics Prelims
- Mathematics under the Microscope
- Mathematics Weblog
- Mathemusicality
- Michi’s Blog
- neverending books
- Noncommutative Geometry
- Polymathematics
- Portrait of the Mathematician
- Quomodocumque
- Reasonable Deviations
- Secret Blogging Seminar
- Sketches of Topology
- Tangled Web
- tcs math
- The Accidental Mathematician
- The Everything Seminar
- The n-Category Cafe
- The Narrow Road
- The Real Sqrt
- The Rising Sea
- The Unapologetic Mathematician
- Theoretical Atlas
- Tim Gowers’s Weblog
- Topological Musings
- What’s New

### Archives

- February 2015
- January 2015
- December 2014
- November 2014
- September 2014
- December 2013
- February 2013
- December 2012
- November 2012
- October 2012
- April 2012
- April 2011
- November 2010
- October 2010
- August 2010
- July 2010
- June 2010
- April 2010
- March 2010
- February 2010
- December 2009
- November 2009
- October 2009
- September 2009
- August 2009
- July 2009
- June 2009
- May 2009
- April 2009
- March 2009
- February 2009
- January 2009
- December 2008
- November 2008
- October 2008
- September 2008
- August 2008
- July 2008
- June 2008
- May 2008
- April 2008
- March 2008
- February 2008
- January 2008
- December 2007
- November 2007
- October 2007
- September 2007
- August 2007

### Tags

### Top Posts & Pages

# Monthly Archives: February 2009

## The Grothendieck Group of Coherent Sheaves on a Variety

Ok, to continue our quest toward the statement of the theorem, we need to explain a few more ideas. Today, we’ll talk about the structure of the Grothendieck group K(X) of coherent sheaves on an algebraic variety X. (Remember the … Continue reading

Posted in AG From the Beginning, Algebraic Geometry
12 Comments

## 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

## Some new math blogs

Clicking around wordpress, I’ve found two new math blogs that seem to have started in the last couple of months. So, go and check out Motivic Stuff and Embûches tissues and welcome them to the blathosphere.

Posted in Uncategorized
Leave a comment

## Direct Image Sheaves Under Proper Maps

Today we continue our review/introduction of background material en route to stating and proving the Riemann Roch theorem. This theorem involves the relationship between proper maps and sheaves on the domain and target, so we need to understand how they … Continue reading

Posted in AG From the Beginning, Algebraic Geometry, Cohomology
7 Comments

## Deligne and Mumford on the Moduli of Curves

Today I’m going to talk a bit about an important paper from 1969. This one. It’s a bit hard to read at some points, but it was revolutionary. In it, Pierre Deligne and David Mumford prove that the moduli space … Continue reading

Posted in Algebraic Geometry, Big Theorems, Curves, Deformation Theory
3 Comments

## The Dual Isogeny

Dear Readers, Today I want to talk about morphisms between curves and the special properties they have. This is sort of a broad-based topic, given that the study of morphisms and their properties is essentially the whole of algebraic geometry. … Continue reading

Posted in Uncategorized
5 Comments

## Proper Maps and (Quasi) Projective Varieties

I’m back! So let’s get down to business. What I really want to talk about is the Riemann Roch Theorem. You may wonder why, since it has already been discussed here , but there have been vast generalizations of this … Continue reading

Posted in AG From the Beginning, Algebraic Geometry
12 Comments