I'd like some introductory references for deformation theory in algebraic geometry. I'm interested in survey articles too but I primarily want references which give all the definitions and go through the basics carefully and also give some idea of the link between deformation theory and intersection theory and/or K-theory. Texts with examples would be particularly nice. Applications to representation theory would also be useful to me.

As a specific example, I would like to understand how deformation theory helps in understanding the geometry of the Hilbert scheme of points on a surface (and the geometry of more general moduli spaces like Nakajima quiver varieties, if possible).

My background in geometry is Hartshorne and some material on constructible sheaves and D-modules. I've also come across some deformation theory from the representation theory side.

Thank you for the help.

Edit: I'm also perfectly happy with references that only deal with complex algebraic geometry.

  • 2
    $\begingroup$ Hartshorne has a book on Deformation Theory too. Have you looked at Greuel, Lossen, Shustin - Introduction to Singularities and Deformations (2007) ? $\endgroup$ – M.G. Feb 5 '16 at 21:49
  • $\begingroup$ I just took a look at it. It's not exactly what I'm looking for but it has some interesting stuff. The appendix looks useful. Thanks. $\endgroup$ – Siddharth Venkatesh Feb 5 '16 at 21:56
  • 1
    $\begingroup$ try Palamodov:mathnet.ru/php/… or some of the other references here: icmat.es/congresos/STM/abstracts/vanStraten.pdf and everyone bases their treatment on the 1964 Harvard PhD thesis of M. Schlessinger $\endgroup$ – roy smith Feb 6 '16 at 0:48
  • 1
    $\begingroup$ Perhaps you may try Eisenbud and Harris forthcoming book: isites.harvard.edu/fs/docs/icb.topic720403.files/book.pdf $\endgroup$ – F Zaldivar Feb 6 '16 at 3:24

You could try Sernesi's book (deformations of algebraic schemes).


Your Answer

By clicking "Post Your Answer", you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.