  An expression for the curvature of the "covariant" determinant line bundle is
given in even dimensional space-time. The usefulness is guaranteed by its
prediction of the covariant anomaly and Schwinger term. It allows a parallel
derivation of the consistent anomaly and Schwinger term, and their covariant
counterparts, which clarifies the similarities and differences between them. In
particular, it becomes clear that in contrary to the case for anomalies, the
difference between the consistent and covariant Schwinger term can not be
extended to a local form on the space of gauge potentials.
