  The $\beta\gamma$ system on the cone of pure spinors is an integral part of
the string theory developed by N. Berkovits. This $\beta\gamma$ system offer a
number of questions for pure mathematicians: what is a precise definition of
the space of states of the theory? Is there a mathematical explanations for
various dualities (or pairings) predicted by physicists? Can a formula for
partition function be written? To help me to answer these questions I use local
algebra in an essential way.
