  Using the generalized hamiltonian method of Batalin, Fradkin and Vilkovisky,
we investigate the algebraic structure of anomalies in the Polyakov string
theory that appear as the Schwinger terms in super-commutation relations
between BRST charge and total hamiltonian. We obtain the most general form of
the anomalies in the extended phase space, without any reference to a two
dimensional metric. This pregeometri- cal result, refered to as the genelarized
Virasoro anomaly, independent of the gauge and the regularization under a minor
assumption, is a non-perturbative result, and valid for any space-time
dimension. In a configuration space, in which the two dimensional metric can be
identified, we can geometrize the result without assuming the weak
gravitational field, showing that the most general anomaly exactly exhibits the
Weyl anomaly.
