Category Archives: Curves

Subvarieties of Jacobians

For this whole post, we’ll take to be a curve and the Jacobian of the curve.  We’re going to construct several special subvarieties (not special in any technical sense, though) of , which encode a great deal of geometric information … Continue reading

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Jacobians of Curves

As promised in the last post, I’m making another go at MaBloWriMo…maybe others will as well.  I don’t know if I’m going to have a coherent topic over the course of this month, but I’ll be starting with abelian varieties … Continue reading

Posted in Abelian Varieties, AG From the Beginning, Algebraic Geometry, Curves, Hodge Theory, MaBloWriMo | Leave a comment

The Schottky Problem (ICTP)

These are my notes, and are only a rough approximation of the actual talk:

Posted in Abelian Varieties, Conferences, Curves, Hodge Theory, ICTP Summer School, Moduli of Curves | 1 Comment

Monodromy and Moduli

Today, we’re going to prove a BIG theorem, but only in the characteristic zero case (we’ll be working over as usual). The theorem is rather tough, and to do it in positive characteristics it’s best done through stacks. Specifically, we’ll … Continue reading

Posted in Algebraic Geometry, Algebraic Topology, Big Theorems, Curves, Deformation Theory, Moduli of Curves | 3 Comments

B-N-R Part 5: Spectral Curves

Today we’re back to some material from the first post in this series, and going to prove an actual theorem about vector bundles.  Next time, we’ll be getting into the heart of the paper, and that may be my last … Continue reading

Posted in Abelian Varieties, Big Theorems, Curves, Vector Bundles | 4 Comments

B-N-R Part 4: Prym Varieties

The last post was on the generalities of Abelian varieties, and constructing a map.  This time, we’re going to do it for a specific one, and the maps involved will all be useful later.  We start out with a finite … Continue reading

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B-N-R Part 3: PPAV’s and some details

Now, we continue our tour through Beauville, Narasimhan, Ramanan.  We’ve talked about Twisted Endomorphisms and we’ve talked about the Generalized Theta Divisor on the Moduli Space of Vector Bundles.  So today we’ll talk a bit about Abelian Varieties, Principal Polarizations, … Continue reading

Posted in Abelian Varieties, Algebraic Geometry, Big Theorems, Curves, Vector Bundles | 2 Comments