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I am studying GW theory (and DT theory) in algebraic geometry. I now understand the heuristic "Aut, Def, Obs" argument written in Mirror Symmetry book (by Hori et al.), but it is too hard for me to read for example "Intrinsic normal cone" by (Behrend and Fantechi). It seems to me that these is a big gap between the heuristic explanation and rigorous arguments in deformation theory in these foundational papers.

Could anyone suggest good background reading materials for this area? I am aware of the standard Hartshorn's book.

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  • $\begingroup$ Have you read any paper by Pandharipande? Maybe start with Fulton-Pand... That one is all about projective schemes and has no stacks in it. Or maybe some early paper by Kai Behrend. $\endgroup$
    – 36min
    Nov 1, 2012 at 5:11
  • $\begingroup$ You could also try Richard Thomas's `A holomorphic Casson invariant...', which is where DT invariants were first introduced. Section 3 is about deformation theory. I haven't actually read it, but it looks like a fairly low-tech introduction tailored to the purpose of DT theory. $\endgroup$
    – Chris Brav
    Nov 5, 2012 at 11:37
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    $\begingroup$ I gave a course on virtual classes last year in Bonn - it was a bit long but self contained, and included the deformation theory. If there's interest I might try to type and tidy up the handouts and put them online. [To the mods: feel free to delete the comment if inappropriate.] $\endgroup$
    – Barbara
    Nov 6, 2012 at 18:33
  • $\begingroup$ there would definitely be interest! $\endgroup$
    – Jacob Bell
    Nov 8, 2012 at 21:05
  • $\begingroup$ I am interested in your handouts too, Barbara! $\endgroup$
    – user2013
    Nov 13, 2012 at 0:58

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