Monthly Archives: September 2008

Rational Varieties — An Introduction Through Quadrics

Projective spaces are the most basic algebraic varieties we know (at least in some sense) and rational varieties are those that are as close as possible to being projective spaces.  Informally, a rational variety is one admitting a parametrization by projective space.  The project of determining which … Continue reading

Posted in AG From the Beginning, Algebraic Geometry | 4 Comments

Resolution in positive characteristic?

Ok, rumor has it that Hironaka is claiming a proof of resolution of singularities in positive characteristic.  Anyone know anything more about this? Do we have any readers at Harvard that can confirm this rumor or squash it? Do I … Continue reading

Posted in Uncategorized | 4 Comments

Toric Geometry I – Definitions

Ok, so I’m going to mostly be posting on toric geometry for the near future, and in particular, working out what we need to do some mirror symmetry with it. I’ll be following various things by David Cox, so check … Continue reading

Posted in Algebraic Geometry, Toric Geometry | 3 Comments

Group Schemes and Moduli (IV)

Unless there is some specific interest, I think this will be the final post in the series about taking quotients of varieties by actions of group schemes.  Recall that everything is being done over an algebraically closed field, .  I’ll … Continue reading

Posted in AG From the Beginning, Algebraic Geometry, Examples | 3 Comments

Oral Exams Result

And the results are in…I got out of the exam less than a half hour ago.  I passed! Whee, I’m now officially a PhD Candidate.  I should be able to resume posting next week, once I’ve finished recovering and done … Continue reading

Posted in Uncategorized | 12 Comments

Group Schemes and Moduli (III)

Finally we’re ready to discuss what sorts of quotients exist when group schemes act on (some) other schemes.  Recall that for simplicity, every scheme/variety/morphism in sight is assumed to be over the spectrum of a fixed algebraically closed field, . … Continue reading

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