Exploring the Foundations of Algebraic Geometry

  • Thread starter Terilien
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The projection of the curve onto the x axis is a double cover of the x axis, ramified at three points, hence is the Riemann surface of the function (x3 - x)1/2, which is the complex plane with two points removed. The genus of this surface is 1. Hence the cubic has no rational parametrization. Similarly the "quartic" curve x4 + y4 = 1 is a double cover of the x - axis ramified at 4 points,
  • #36
for those naturally daunted by the large amount of prerecquisites i laid out for alg geom, try miles reid's little book, undergraduate algebraic geometry. it requires very little background, probably only stuff many of you already have, and yet does some really good geometry.
 
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  • #37
by the way "my" birthday algebraic geometry conference at UGA was just an unbelievable high, with wonderful young geometers from all over the world, and old friends too. may you all have such good friends as the young people who put this on and did all the work, as well as the friends who came from distant places to wish us well at UGA, and help us with our program.

Our young grad students got to meet people from the best places in the world, and make friends and contacts that should help them for years. Those if you hoping to become amthematicians should take note and try to attend good conferences as soon as possible in your career.

In my case too, I realized I had been falling way behind the current trends and language in my own area by staying home too much and not interacting and listening to top people talk. So I got a tremendous boost and have been thinking about live questions all weekend and also since they left yesterday.

It is really hard to believe how generous these people are, since they all left home and families and traveled to be there, and some of them also had to miss the final four games!

You young kids who are wondering how in the heck you learn all this stuff, well you do it by listening to people talk who know the stuff well. This is much more efficient than trying to plow through books. An expert can tell you in in one minute the key idea behind a difficult topic, that would take you a very long time to get through alone.now i have to force myself to log off, quit lallygagging here, pleasant as it is, and actually think about a little question someone asked me yesterday.
 
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  • #38
ok i solved it.
 

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