### 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

- AG from the Beginning
- Projective Varieties
- Linear Systems
- The Twenty-Seven Lines on the Cubic Surface
- Some Commutative Algebra and a bit of Geometry
- The Hilbert Polynomial
- The Veronese Embedding
- Affine Varieties
- Weil Divisors, Cartier Divisors and more Line Bundles.
- Schubert Classes and Cellular Cohomology

# Monthly Archives: September 2008

## Rational Varieties — An Introduction Through Quadrics

Projective spaces are the most basic algebraic varieties we know (at least in some sense) and rational varieties are those that are as close as possible to being projective spaces. Informally, a rational variety is one admitting a parametrization by projective space. The project of determining which … Continue reading

Posted in AG From the Beginning, Algebraic Geometry
4 Comments

## Resolution in positive characteristic?

Ok, rumor has it that Hironaka is claiming a proof of resolution of singularities in positive characteristic. Anyone know anything more about this? Do we have any readers at Harvard that can confirm this rumor or squash it? Do I … Continue reading

Posted in Uncategorized
4 Comments

## Toric Geometry I – Definitions

Ok, so I’m going to mostly be posting on toric geometry for the near future, and in particular, working out what we need to do some mirror symmetry with it. I’ll be following various things by David Cox, so check … Continue reading

Posted in Algebraic Geometry, Toric Geometry
3 Comments

## Group Schemes and Moduli (IV)

Unless there is some specific interest, I think this will be the final post in the series about taking quotients of varieties by actions of group schemes. Recall that everything is being done over an algebraically closed field, . I’ll … Continue reading

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

## Oral Exams Result

And the results are in…I got out of the exam less than a half hour ago. I passed! Whee, I’m now officially a PhD Candidate. I should be able to resume posting next week, once I’ve finished recovering and done … Continue reading

Posted in Uncategorized
12 Comments

## Group Schemes and Moduli (III)

Finally we’re ready to discuss what sorts of quotients exist when group schemes act on (some) other schemes. Recall that for simplicity, every scheme/variety/morphism in sight is assumed to be over the spectrum of a fixed algebraically closed field, . … Continue reading