I saw Christian Haesemeyer give a (great) talk in which he used this symbol (without comment), so I know other people (topologists?) also think in this way. But I looked on detexify, and there isn’t such a latex symbol! ]]>

Also, as you know, Pryms are generally quite hard to write down (as is any abelian variety), but last summer I thought about them and the Donagi(-Smith) construction for a little bit and there’s an instance where you can easily write them down. It’s actually outside of the usual etale double-covers domain of Prym varieties, but it works.

Any map from a genus two curve to a genus one curve has to be ramified at two (geometric) points. If the bottom curve is indeed an elliptic curve, we have to be able to write our genus two curve as

$

and our genus one curve as

$

This even works arithmetically, see papers of Everett Howe.

What then is the “Prym” for this map? Why it’s just the other curve that we map down to from our genus 2, namely

$$

This comes up in a few fun places, such as elliptic curves of conductor 26, 38 and 58, where this double cover is in fact the modular map out of a Shimura curve.

… Hopefully that somewhat rambling comment fits in with the general “Here’s something cool!” feel of this blog.

]]>Thanks for the link too; incidentally, there are two pretty good ways to find math blogs: mathblogging.org and n-cat’s large list of math blogs. (I have a folder in my rss reader that has, basically, all math blogs.)

]]>Anyway, glad to see anther blogger! Hope you keep it up. There is a good math blog over at The Math Less Traveled, since you seem to be into that kind of stuff.

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