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.
About this blog
This blog started out as a group blog about random parts of math, then evolved into a solo blog used primarily for studying for my (Charles) oral exam. Now, it's changing into a group blog in algebraic geometry, with me, Charles Siegel, Matt DeLand, and Jim Stankewicz currently contributing.Pages
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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.
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 (GriffithsHarris book) of the generic word in AG but it’s too technical.
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.
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.
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.
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 mean?
Also, after how many years (if any) of grad school did you take those oral exams?
Thanks
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 on a curve is a linear system of dimension and degree . So it maps the curve to a degree curve in .
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.
October 14, 2009 at 9:58 am
For rings, we say that is essentially of finite type as an algebra if it is a localization of a finitely generated 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 is noetherian, then is, so my thought is that a scheme, essentially of finite type over a locally noetherian scheme should also be locally noetherian.
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 preordered list, a lattice) of those blog entries?
I would want to start kind of inbetween 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!
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.
August 23, 2010 at 5:19 am
Hi,
I have a question about proper maps: if f: Y −→ Z is a proper beetween quasi projective varieties and let
X ⊂ Y such that the restriction of f to X is again proper is the embedding of X into Y proper?
Thank you
October 23, 2010 at 8:30 pm
@Matteo: An immersion is proper iff it is closed.
June 8, 2011 at 11:55 am
Just wanted to drop a note to say I’ve been finding your AG from the beginning blog posts extremely helpful in my own studies, thank you for such a readable introduction to AG!
September 20, 2012 at 7:31 am
Hello Charles,
I want to thank you for the excellent work you have done through your blog. It has made my life a lot more comfortable tackling the demon that is Algebraic geometry.
I would really love it if you could write a similar blog for Commutative algebra, as it is a subject that is quite often ignored a thorough treatment when instructors teach algebraic geometry.
September 22, 2012 at 6:45 am
Well, I am preparing to return to blogging (watch for a post in about a week) though my plan was a bit more analytic in nature. I’m more on the analytic side of algebraic geometry, that draws from complex analysis, differential geometry and algebraic topology as the main tools. However, and I know this is a comment so it won’t be noticed as much, if other people are interested in some sort of “commutative algebra from the beginning” series, trying to be informal and talk about the intuition behind commutative algebra constructions and theorems and connecting them to algebraic geometry, reply here, and I might do it.
October 9, 2012 at 9:02 am
“trying to be informal and talk about the intuition behind commutative algebra constructions and theorems and connecting them to algebraic geometry”
That sounds absolutely perfect, if you have the time. Your AG from the Beginning series is great by the way!
March 29, 2014 at 5:16 am
comment 3 on this page :http://rigtriv.wordpress.com/2009/11/03/chernclassespart1/ is spam and not something authorised by the linked company. appreciate removal help.
March 29, 2014 at 8:06 pm
Removed, I haven’t been maintaining the blog for awhile, so the comment hygiene has declined. Apologies.