I have recently posted the latest pdf version (dated October 21, 2025) in the usual place. This preprint version has (with trivial exceptions) the same content as the published version, although the pagination and formatting are different, and it is not as beautiful. Because people may use different versions, I strongly encourage everyone to refer [ ]
I am now in a particularly busy period of this temporary new life where a good deal of my time is spent in service of mathematics through the American Mathematical Society. I m typing this en route from the University of Virginia (where I met a number of impressive students and postdocs, and chatted with great [ ]
The current (September 8 2024) version is posted at the usual place. I think this will be the final version I will post until the version that is equivalent in content to the published version. I suspect that will be some time in the new year. There aren t many serious changes. For example, I ve finally [ ]
A new version of the notes (dated July 27 2024) is available at the usual place , and as usual it supersedes all previous versions. This is the version sent to Princeton University Press, so I will now have to be very careful about versioning, since there are now two independent versions in existence (one [ ]
I had heard that there was an elementary proof that a hypersurface (i.e. in affine space over a field) is normal if and only if it is , but I did not know of an argument, and couldn t think of an argument. I think Sándor Kovács told me an argument, but I managed to lose [ ]
A new version of the notes is available at the usual place (the February 21 2024 version). Everything is in potentially nearly final form for an official version , except for typesetting/formatting and the index. (a) Significant change, but not substantive: The figures are now basically done (meaning: redone). Because I think people should be comfortable [ ]
A new version of the notes is available here. (It, and all older versions, are available at the usual place.) I don t have much to report, but I just wanted to post the current version as it continues to converge. Please do continue sending in comments, particularly in the next month. There is a good chance that [ ]
A new version of the notes is available here. (It, and all older versions, are available at the usual place.) The main change from the previous version: The index is potentially done. Now the editing I will do will be primarily in response to comments and suggestions from others. I am very interested in any [ ]
A new version of the notes is available here. (It, and all older versions, are available at the usual place.) For the first time, I would say that the content and editing is potentially done . All content is potentially polished. (Not done: beautification issues e.g. fighting with latex over line breaks. And the index is [ ]
A new version of the notes is available here. (It, and all older versions, are available at the usual place.) Supravat Sarkar kindly pointed out that my Chevalley s Theorem proof was still flawed at the very last step. I have now, I think (again!) fixed it. See Section 8.4.4 for that.