Monthly Archives: May 2008

Serre Duality

Posted on May 29, 2008 by Charles Siegel

Sorry that this one is late, things are going to continue to be hit-or-miss through June, though hopefully hit more than miss. Anyway, we’ve got a cohomology theory for sheaves. Anyone who has worked with cohomology of manifolds will know … Continue reading →

Posted in AG From the Beginning, Algebraic Geometry, Big Theorems, Cohomology | 2 Comments

Cohomology of Sheaves

Posted on May 26, 2008 by Charles Siegel

In order to get at surfaces, we don’t just need the scheme theory of the last two posts, but we also need to understand the cohomology of sheaves. We will not be proving all of the details, we will also … Continue reading →

Posted in AG From the Beginning, Algebraic Geometry, Cohomology | Leave a comment

Proj of a Graded Ring and Basic Properties of Schemes

Posted on May 23, 2008 by Charles Siegel

Last time, we talked about , which takes rings and gives us affine schemes in a manner analogous to affine varieties. Now, though it is safe to say that projective varieties are schemes (well, with the extra points taken into … Continue reading →

Posted in AG From the Beginning, Algebraic Geometry | 6 Comments

Schemes

Posted on May 21, 2008 by Charles Siegel

Sorry about the extended delay, should be back to regular Monday-Wednesday-Friday updates now. I hope. Anyway, we’re going to be heading into Intersection Theory soon, and in particular we’re going to be looking at surfaces. Sadly, at this point, abstract … Continue reading →

Posted in AG From the Beginning, Algebraic Geometry | 7 Comments

New math blog!

Posted on May 7, 2008 by Charles Siegel

A friend of mine from undergrad days has started up a math blog recently. He’s just getting started, but I, at least, expect him to do interesting things once he gets rolling (probably in another week or so, due to … Continue reading →

Posted in Uncategorized | 1 Comment