# Torelli Over an Algebraically Closed Field

I was originally going to do this post in wordpress but then instead I’m just posting Torelli over k bar; a rough outline based on a proof in Polishchuk’s book.

But I wanted to add some notes here. At some point I reference this post about chapter 17 in Polishchuk.

Extensively in the proof base change is used. This says if there is a diagram

where and if flat and is proper then there is an isomorphism

as are flat they don’t need to be derived (Huybrechts pg 85). As an application consider three schemes and a map . Note is flat. Let and consider .

This gives . Also . So

(proj. form.)

This is the result for

There are similar stories for

## About this entry

You’re currently reading “Torelli Over an Algebraically Closed Field,” an entry on Math Meandering

- Published:
- May 21, 2010 / 2:23 am

- Category:
- Uncategorized

- Tags:
- base change, Fourier-Mukai, Polishchuk, Torelli

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