### 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
May 2017 S M T W T F S « Feb 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 ### Recent Comments

Francisco Palmios on Gradings of Rings and Mod… Anonymous on The Veronese Embedding Varieties and Scheme… on Schemes Varieties and Scheme… on Abstract Varieties Rena on Sheaves ### 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

# Category Archives: Big Theorems

## The Grothendieck-Riemann-Roch Theorem, Stated

Suppose you have a proper map between smooth (quasi) projective varieties. Then suppose you have a coherent sheaf on . After viewing that sheaf as an element of the Grothendieck Group of coherent sheaves on , there are two things … Continue reading

## 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

## Kontsevich’s Formula

This is my last post of 2008, so happy holidays to everyone!. This one shouldn’t take too long, it’s just applying the lessons of the last few posts to compute some numbers. We start by talking like physicists. We’ll write … Continue reading

## Request: Projective Elimination Theory

We talked before about elimination theory, doing it entirely in the affine case. The question was asked about how to do it projectively. There are a couple of subtleties to it, but the idea is simple: we eliminate in each … Continue reading

## Geometric Form of Riemann-Roch

Now, the way that the Riemann-Roch theorem was phrased before, the geometry wasn’t obvious. We had to extract it in terms of rational functions with poles given by a divisor. Now that we’ve talked about canonical curves, we can use … Continue reading

## Hurwitz’s Theorem on Automorphisms

This is this blog’s 100th post. Now, not quite my hundredth, nor nearly the hundredth with actual math content, but still, it’s a number which, when expressed in base ten, happens to have some zeros. More importantly, however, tomorrow marks … Continue reading

Posted in AG From the Beginning, Algebraic Geometry, Big Theorems, Curves
1 Comment

## Hurwitz’s Theorem

Ok, back to curves. We’d wandered a bit in the direction of this topic before, having discussed Bezout’s Theorem and the Riemann-Roch Theorem. Today we’ll talk about the Hurwitz formula, also called the Riemann-Hurwitz formula. It’s a rather nice result, … Continue reading

Posted in AG From the Beginning, Algebraic Geometry, Big Theorems, Curves
1 Comment