We’re a group of graduate students in mathematics at several universities just starting out. We’ve all found some interesting things floating out there that no one seems to know about, or just that we’d like a good place to post a rant about.
Editor reviews are provided by professional editors who evaluate a blog based on the following criteria: Frequency of Updates, Relevance of Content, Site Design, and Writing Style.
Well, really, for intersection theory, it’s true. We start with a closed subscheme, with normal cone . We’re going to construct a family of embeddings that deforms to the zero section of . Then, because intersections should vary nicely in...
So, last time we talked about Segre classes and cones. Now, we’re going to move ahead, and talk about a specific cone in detail, the Normal cone we defined on Monday. Let be a subscheme, and let be its normal cone. We define , the Segre class...
Last time, we talked about the Normal Cone. We’re going to go back a bit and increase the generality before coming back to it. Let be a cone over , and let be the projective closure. We define the Segre class of the cone , in to be , where ...
Ok, so I took the weekend off to figure out where things are going and get a bit ahead. Will probably be doing that all month. So now, we’re going to talk about cones and normal cones, with the goal of eventually defining the intersection product...
Today, we’re going to construct a ring that encodes quite a lot of intersection data (though not terribly transparently) as well as some special combinations of Chern classes. A lot of modern intersection theory and enumerative geometry takes place...
