18th International Symposium, AAECC-18
Tarragona, Spain, June 8-12, 2009
Proceedings
In 1998 J.P. Hansen considered algebraic geometry codes defined over toric surfaces. Thanks to combinatorial techniques of such varieties he was able to
estimate the parameters of the resulting codes. For example, the minimum distance
was estimated using intersection theory. Toric geometry studies varieties
which contain an algebraic torus as a dense subset and where moreover the torus
acts on the variety. The importance of such varieties, called toric varieties, resides
in their correspondence with combinatorial objects, which makes the techniques
to study the varieties (such as cohomology, intersection theory, resolution of
singularities, etc) more precise and at the same time tractable