Suggestions and Requests

Here is a place to post suggestions, topic requests, and in particular, papers (old or new) that fit the general feel of the blog (whatever that is) and would be good topics for discussion.  We’ll see how this goes.

11 Responses to “Suggestions and Requests”

  1. thoughtcounts A Says:

    August 21, 2008 at 2:04 pm

    Just a note – I’m hosting the next Carnival of Mathematics at thoughtcounts.net tomorrow. The carnival page lists no host, so I have a lower than usual number of submissions. If you have anything to submit, I’d love to hear from you.

    Reply
  2. Antonio Says:

    April 12, 2009 at 11:55 am

    Hi, I’m an undergraduate student and I’m interested in AG. Now that I began to read some books I found very often the word “generic”. So I think it would be nice if someone post a blog about it. I found a definition (Griffiths-Harris book) of the generic word in AG but it’s too technical.

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  3. Charles Siegel Says:

    April 12, 2009 at 12:10 pm

    Well, I can give you it roughly here (a longer post will follow when I can find the time). In AG, open sets are always dense (well, in irreducible things). So generic will generally mean that something holds for an open set on the space of all such objects, and occasionally it will mean the countable intersection of open sets. Think that it means that away from some variety (ie, there are some polynomial equations saying when it fails) something is ok, though you might have to deal with a variety with countably many irreducible components.

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  4. Antonio Says:

    April 12, 2009 at 1:57 pm

    Thank you so much for your help. I hope you find the time soon. I’ll be waiting for it.

    Reply
  5. John Armstrong Says:

    April 12, 2009 at 4:54 pm

    I tend to think of “generic” as meaning “it stays the same when you wiggle it”.

    Two curves being tangent is not a generic intersection. Wiggle them a bit and a crossing tangency becomes a simple crossing, or a noncrossing tangency either becomes a pair of crossings or vanishes entirely.

    On the other hand, two curves crossing is generic, since if you wiggle them a bit they’ll still cross.

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  6. Dragos Says:

    May 17, 2009 at 9:33 am

    Hi Charles,
    I’ve looked on your page at the oral exams: can you please tell me what do g_r^d mean?
    Also, after how many years (if any) of grad school did you take those oral exams?
    Thanks

    Reply
  7. Charles Siegel Says:

    May 17, 2009 at 10:15 am

    I took my oral exams right at the beginning of my second year. And here’s a quick answer, a g^d_r on a curve is a linear system of dimension d and degree r. So it maps the curve to a degree r curve in \mathbb{P}^d.

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  8. PeterG Says:

    October 12, 2009 at 7:02 am

    Hi, Charles,

    What is “essentially of finite type morphism” (from Koll’ar’s book)? If a scheme is “essentially of finite type” over a locally noetherian scheme, does it imply, that it is also locally noetherian? Sorry for presumably trivial question.

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  9. Charles Siegel Says:

    October 14, 2009 at 9:58 am

    For rings, we say that R is essentially of finite type as an S-algebra if it is a localization of a finitely generated S-algebra. So presumably, for schemes, it would mean that this holds on affines, and perhaps require that the map is affine to make it work out, haven’t thought it through very deeply.

    Now, this says that if S is noetherian, then R is, so my thought is that a scheme, essentially of finite type over a locally noetherian scheme should also be locally noetherian.

    Reply
  10. Konrad Says:

    October 21, 2009 at 11:59 pm

    Have you collected all your “AG from the beginning” posts somewhere?

    I have tried to use some kind of search on this blog but the results didn’t satisfy me. So maybe you could just assemble an ordered list (or a pre-ordered list, a lattice) of those blog entries?

    I would want to start kind of in-between but I don’t know where… and the old postings don’t link to the newer ones..

    By the way: thanks for having already written so much useful stuff!

    Reply
  11. Charles Siegel Says:

    October 22, 2009 at 6:52 am

    They’re in the category “AG from the Beginning” but I guess I’ll make a page, and then whenever I do something somewhat basic, I’ll link to it there.

    Reply

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