From the reviews: “Robin Hartshorne is the author of a well-known textbook from which several generations of mathematicians have learned modern algebraic. In the fall semester of I gave a course on deformation theory at Berkeley. My goal was to understand completely Grothendieck’s local. I agree. Thanks for discovering the error. And by the way there is another error on the same page, line -1, there is a -2 that should be a
|Published (Last):||20 November 2012|
|PDF File Size:||14.72 Mb|
|ePub File Size:||1.55 Mb|
|Price:||Free* [*Free Regsitration Required]|
We could also interpret this equation as the first two terms of the Taylor expansion of the monomial.
Algebraic geometry Differential algebra. So the upshot is: Thanks for discovering the error.
The intuition is that we want to study the infinitesimal structure of some moduli space around a point where lying above that point is the space of interest.
This is now accepted as proved, after some hitches with early announcements.
These obviously depend on two parameters, a and b, whereas the isomorphism classes of such curves have only one parameter.
One might think, in analogy, of a structure that is not completely rigid, and that deforms slightly to accommodate forces applied from the outside; this explains deforation name. Post as a guest Name.
Seminar on deformations and moduli spaces in algebraic geometry and applications
Krish Here is one version: Why on earth should we care about fat points? It’s not in the link I gave above.
That formulation is false. Everything is done in a special case and shown to follow from basic algebra. You are thoery to ask more questions as soon as you read more about it! From Wikipedia, the free encyclopedia.
Sign up or log in Sign up using Google. What follows is harfshorne attempt to motivate this beautiful and difficult in my opinion subject. I am just writing my comment as an answer. As it is explained very well in Hartshorne’s book, deformation theory is: For genus 1, an elliptic curve has a one-parameter family of complex structures, as shown in elliptic function theory.
This is true for moduli of curves. Versal Property Local Deformation Space Mini-versal deformation space I came across these words while studying these papers a Desingularization of moduli varities for vector bundles on curves, Int. There was also an MSRI workshop some years ago; I think the videos are still online and there is a draft of a book written by the organizers floating around the web.
For our monomial, suppose we want to write out hartshornw second order defomation, then. Hence there must be an equation relating those a and b which describe isomorphic elliptic curves.
Deformation theory – Wikipedia
Babai 2, 2 15 So it turns out that to deform yourself means to choose a tangent direction on the sphere. This page was last edited on 31 Octoberat Deformation theory was famously applied in birational geometry by Shigefumi Mori to study the existence of rational curves hartshornf varieties.
The infinitesimal conditions are therefore the result of applying the approach of differential calculus to solving a problem with constraints. Infinitesimals have long been in use by mathematicians for non-rigorous arguments in calculus.