Singular locus

Near we want to have the BRST transformation of the form:

This means that we should have action of the first order, and remember
I also want holomorphic:

If we had action like then
we would have something like which is not what we want!
It is essential to have the action of the first order. In practice, the leading term comes out like
; to make
it of the order we rewrite

The other fields are of the higher order:

with some quadratic form . For we need:

In the pure spinor formalism we put (the Gamma-matrices)