Daniel Murfat has a nice series of notes on various mathematical topics, mostly algebraic geometry.

For mathematical sociologists, network people and statisticians: A lecture by CMU’s Stephen Feinberg on using algebraic geometry to study p1 network models. ...

I have blogged a number of times in the past about the relationship between finitary (or “hard”, or “quantitative”) analysis, and infinitary (or “soft”, or “qualitative”) analysis. One way to connect the two types of analysis is via...

They come out of thin categorical air.

This post is about a computation every algebraic geometry student should do, but that none of my courses covered. Let be a smooth, projective curve over . Then is a one dimensional -vector space. If you’ve read Hartshorne III.7 ca...

A comment-thread well worth following while on vacation was Algebraic Geometry without Prime Ideals at the Secret Blogging Seminar. Peter Woit became lyric about it : My nomination for the all-time highest quality discussion ever...

In algebraic geometry, the Nullstellensatz gives an algebraic characterization of when a multivariate polynomial vanishes on a set of points defined by a system of (complex) polynomial equations. I’ve just come across an analogue of...

Since I’m not sure these links are well-known (i.e., I didn’t know them myself until yesterday in one case, and until a few weeks in the other), it may be useful to point them out: The work-in-progress new edition of SGA 3 (the par...

So let's say you have two varieties Z(f) and Z(g) (I'm using Hartshorne's notation here - these are, just for clarity's sake, the zero sets of the polynomials f and g), with f and g irreducible. Then I(Z(f)) = and I(Z(g)) = . What'...

The first definition in “Grothendieck-style” algebraic geometry is the affine scheme for any ring . This is a topological space whose set of points in the set of prime ideals in . Then one defines a scheme to be a locally ringed ...

The Grothendieck circle is a great resource to find published as well as unpublished texts by Alexander Grothendieck. One of the text I was unaware of is his Introduction to Functorial Algebraic Geometry, a set of notes written up ...

Hey guysI'm looking for a proof of the following theorem:The total Gaussian curvature of an oriented surface M in R^3 equals the algebraic area of the image of its Gauss map. I've checked in O'Neill's Diff Geom, and while he states ...

As far as academics are concerned, summer has started, which means that there are lots and lots of conferences going on. The past couple weeks we’ve had two here in the Columbia math department, one in algebraic geometry, and anoth...

Hirzebruch's problem at the interface of topology and algebraic geometry has occupied mathematicians for more than 50 years. A professor of mathematics at the Ludwig-Maximilians-Universitaet in Munich has now solved this problem con...

You can now see the introduction to a paper James Dolan is writing about algebraic geometry for category theorists. You can also see 5 lectures he gave on this topic.

This is not a question of authorship, à la Rembrandt. Rather, to be blunt, the question is: is this person the founder of modern algebraic geometry? Is it the creator of the étale fundamental group who hands over bottles to acolyte...

There will be a school on Homotopy Theory and Algebraic Geometry in Seville from September 7th to 13th, 2009.

William Fulton has made his book, Algebraic Curves, available for download. Fulton’s book is a classic exposition of algebraic geometry at the level of an advanced undergraduate. It is one of the few undergraduate texts that cover...

Toric varieties are among the simplest objects in algebraic geometry, and they are often a test case for general conjectures. One of the great things about them is that you can completely describe a toric variety by combinatorial da...

When I first tried to read Griffiths and Harrris’s Principles of Algebraic Geometry, I was baffled by formulas like . The absolute value function wasn’t analytic, so its derivative with respect to wasn’t defined. And what were all ...