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

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The intuition is that we want to study the infinitesimal structure of some deformahion space around a point where lying above that point is the space of interest. Maxim Kontsevich is among those who have offered a generally accepted proof of this. Infinitesimals can be made rigorous using nilpotent elements in local artin algebras.

It is just an attempt, I cannot promise it will be useful. Post as a guest Name.

hartshrone By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. One expects, intuitively, that deformation theory of the first order should equate the Zariski tangent space with a moduli space. 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.

I think the workshop you mentioned is the following one: This is true for moduli of curves. In the case of genus 0 the H 1 vanishes, also. This was put on a firm basis by foundational work of Kunihiko Kodaira and Donald C. There is an obstruction in the H 2 of the same sheaf; which is always zero in case of a curve, for general reasons of dimension. Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

I’ll tell you later what nice group describes these objects! For genus 1 the dimension is the Hodge number h 1,0 which is therefore 1.

I came across these words while studying these papers a Desingularization of moduli varities for vector bundles on curves, Int. I have tried reading few lecture notes, for example: Here is MSE copy: Sign up using Thdory.

### Deformation theory – Wikipedia

This page was last edited on 31 Octoberat I guess in the process of understanding I will come hartzhorne with more questions. In other words, deformations are regulated by holomorphic quadratic differentials on a Riemann surface, again something known classically.

Email Required, but never shown. And by the way there is another error on the same page, line -1, there is a -2 that should be a Now let me tell you something very naive. Spencerafter deformation techniques had received a great deal of more tentative application in the Italian school of algebraic geometry. If we have a Galois representation.

I am just writing my comment as an answer. May be I am missing thekry points for understanding. Another method for formalizing deformation theory is using functors on the category of local Artin algebras over a field.

So after several repetitions of the procedure, eventually we’ll obtain a curve of genus 0, i.

## Deformation theory

From Wikipedia, the free encyclopedia. Thank you for your elaborate answer. Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

The hteory of the proof later became known as Mori’s bend-and-break. Brenin I have now some idea about deformation. MathOverflow works best with JavaScript enabled. One of the major applications of deformation theory is in arithmetic. Sign up or log in Sign up using Google.