Posted by Martin Orr on Tuesday, 20 May 2014 at 19:30
I have decided to play around with creating some maps using the freely available data from OpenStreetMap. I am mainly interested in creating maps of London bus routes but first I had to learn how to use the Tilemill rendering software and how to load OpenStreetMap data into Tilemill. In this post I will describe how I rendered my first map, a very simple line map of London.
Posted by Martin Orr on Friday, 09 May 2014 at 18:25
In the last post we showed that extensions of an abelian variety 
by the additive group 
.
In this post I will show that there is a so-called universal vector extension of , that is, a vector extension 
of such that every vector extension of can be obtained in a unique way as a pushout of .
The vector group part of is 
, and an ingredient which we require from last time is that this is finite-dimensional.
Even if you are not interested in vector extensions of abelian varieties for their own sake (and I am not), they still have interesting properties. For example, I will show that they provide examples of algebraic varieties over the complex numbers which are non-isomorphic as algebraic varieties but which are isomorphic as complex manifolds.