### 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 2015 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

Juan on The hyperbolic plane Algernon on So…umm…I’m a… beck (@toorandom) on Understanding Integration III:… David Speyer on The sound you hear is another… Anonymous on The Twenty-Seven Lines on the… ### 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
- The Veronese Embedding
- Normalization and Normal Varieties
- Weil Divisors, Cartier Divisors and more Line Bundles.
- Direct Image Sheaves Under Proper Maps
- Locally Free Sheaves and Vector Bundles
- Linear Systems
- Group Theory and Physics
- The Chow Ring and Chern Classes
- Hurwitz's Theorem

# Category Archives: AG From the Beginning

## The Gauss Map

Posting is slowing down a bit, I’ve got a paper I’m trying to get out, and a couple of projects that are hitting some preliminary results, plus, I’m getting ready for holiday travel, and then two months at Humboldt. Trying … Continue reading

## Understanding Integration III: Jacobians

Now, we’re going to talk a bit about the geometry of the periods, which were completely analytic in nature. As we mentioned, for a compact Riemann surface , we have a period matrix that encodes the complex integration theory on … Continue reading

## Understanding Integration II: 1-Forms and Periods

Last time, we discussed integration theory of functions along paths on Riemann surfaces, and then we decided that we wanted to talk about compact Riemann surfaces. Unfortunately, there aren’t any holomorphic functions on them, and meromorphic functions are the wrong … Continue reading

## Understanding Integration I: Riemann Surfaces

I’m back! And now, posting from Kavli IPMU in Japan. Now, I’m going to start a series on theta functions, Jacobians, Pryms, and abelian varieties more generally, hopefully with some applications, with my goal being at least one post a … Continue reading

## Prym Varieties

Let be an unramified double cover, where is geneus . Then has genus by the Riemann-Hurwitz formula. Now, encodes lots of information about the geometry of , especially with the additional data of the theta divisor. It turns out that … Continue reading

## Rational Normal Scrolls

Today, we’re going to talk about a very important class of rational varieties, that show up all the time, in quite a variety of different contexts, and at the end, we’ll talk about why.

## Determinantal Varieties

Let be the projectivization of . Then for all , we have a variety given as the set of matrices of rank at most , which is given by the vanishing of the determinents of minors. We call these the … Continue reading