### 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

#GrothendieckTopos s… on Algebraic Geometry Belongs to… #GrothendieckTopos s… on Sheaves on Sites Dennis on Plücker Formulas Farid on Projective Varieties ianmarqz on Mapping Class Group Eleme… ### 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

- AG from the Beginning
- Locally Free Sheaves and Vector Bundles
- Linear Systems
- Normalization and Normal Varieties
- The Chow Ring and Chern Classes
- The Veronese Embedding
- Differential Forms and the Canonical Bundle
- Weil Divisors, Cartier Divisors and more Line Bundles.
- The Twenty-Seven Lines on the Cubic Surface
- Integrable Systems

# Monthly Archives: April 2008

## Next Topic and Hiatus

Ok, so with the overwhelming majority of one vote, the next thing I talk about will be algebraic surfaces and intersection theory. However, first I need to do a bit of reading on this topic, as well as finishing up … Continue reading

Posted in Uncategorized
Leave a comment

## Ok, now I’m annoyed

I’ve generally been well-behaved about focusing on the math on this blog rather than going off into politics or whatever, but sometime while I was at my office today, someone went around campus and put up posters for Ben Stein’s … Continue reading

Posted in Uncategorized
5 Comments

## Linear Systems

Ok, so last time, we discussed divisors. We’re going to keep going in that direction now, and now we’re going to talk about linear systems of divisors. Whenever we talk about linear systems, we’ll assume that our variety is nonsingular, … Continue reading

Posted in AG From the Beginning, Algebraic Geometry
7 Comments

## Weil Divisors, Cartier Divisors and more Line Bundles.

Some people might say that the natural place for this topic is before talk of differential forms and of the canonical bundle, but I disagree. Well, really it’s fine either way, but this is my blog, so I’m going to … Continue reading

Posted in AG From the Beginning, Algebraic Geometry
7 Comments

## Differential Forms and the Canonical Bundle

We’re going to need to start out the day with a bit of algebra, because we’re going to talk about differential forms. Once we have forms, we’ll make a sheaf out of them, and then we’ll use this sheaf to … Continue reading

Posted in AG From the Beginning, Algebraic Geometry
14 Comments

## Line Bundles and the Picard Group

We’ve now talked about vector bundles and locally free sheaves, we’re going to specify to the nicest case: rank 1. We’re generally going to ignore the distinction between the sheaf and the line bundle.

Posted in AG From the Beginning, Algebraic Geometry
12 Comments

## Locally Free Sheaves and Vector Bundles

Last time, we talked about sheaves of modules, and focused on the correspondence between sheaves of ideals and subvarieties. We were talking about the internal geometry of the variety. Today, we’ll talk a bit about more external geometry. Specifically, we’ll … Continue reading

Posted in AG From the Beginning, Algebraic Geometry
8 Comments