  Holomorphic diffeomorphism anomalies of $2\,n$ dimensional gravitational
theories in Beltrami parametrisation (Kodaira-Spencer anomalies) are computed
in the BRST framework, using an extension of the Stora-Zumino method. This
method, which allows to compute anomalies in a very concise way, makes manifest
the topological origin of anomalies. They have a clear geometric
interpretation, since they are expressed in terms of Chern polynomials and
Pontryagin invariants. The key ingredient is the formulation of the BRST
transformations in terms of polyforms, whose total degree is the sum of the
form degree and of the ghost number. This approach simplifies significantly the
analysis available in literature and it allows to compute many other solutions.
Namely, an anomaly, which was computed using different methods, is proved to be
a consistent BRST anomaly, disproving a conclusion in a previous analysis.
