# DEFORMATION THEORY HARTSHORNE PDF

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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Brenin I have now some idea about deformation. 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. Here is MSE copy: Home Questions Tags Users Unanswered.

Thanks for discovering the error. Some characteristic phenomena are: One of the major applications of deformation theory is in arithmetic. For genus 1 the dimension is the Hodge number h 1,0 which is therefore 1. Still many things are vague to me.

I am not accepting the answer yet as someone might come up with a more illuminating answer. Some of the above mentioned notes say that deformation theory is somehow related to Moduli Theory.

## Deformation theory

Why on earth should we care about fat points? As it is explained very well in Hartshorne’s book, deformation theory is: Maxim Kontsevich is among those who have offered a generally accepted proof of this. So after several repetitions of the procedure, eventually we’ll obtain a curve of genus 0, i. Now let me tell you something very naive.

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Robin Hartshorne 2. So it turns out that to deform yourself means to choose a tangent direction on the sphere.

### Seminar on deformations and moduli spaces in algebraic geometry and applications

May be I am missing some points for understanding. In some form these considerations have a history of centuries in mathematics, but also in physics and engineering. This is true for moduli of curves. For genus 1, an elliptic curve has a one-parameter family of complex structures, as shown in elliptic function theory. Home Questions Tags Users Unanswered. I do not have the book in front of me, but it sounds to me like the formulation above is false.

### Deformation theory – Wikipedia

Replacing C by one of the components has the effect of decreasing either the genus or the degree of C. I am just writing my comment as an answer. In the case of genus 0 the H 1 vanishes, also.

I have tried reading few lecture notes, for example: Zima 3 A glimpse on Deformation theory by Brian Osserman 4 Robin Hartshorne’s book on Deformation Theory Nothing helped me to understand what is deformation theory actually.