  Added lemma provided by Michel Brion. Other (minor) changes. Submitted
version.
  Let k be any field, let X' be a projective and geometrically integral
k-scheme and let Y' be a finite closed subscheme of X'. If f: Y'-> Y is a
schematically dominant morphism between finite k-schemes and X is obtained by
pinching X' along Y' via f, we describe the kernel (and, in certain cases, the
cokernel) of the induced pullback map Br_{1}X -> Br_{1}X' between the
corresponding algebraic (cohomological) Brauer groups of X and X'_solely_ in
terms of the Brauer groups of the residue fields of Y and Y' and the Amitsur
subgroups of X and X' in Br k. As an application, we compute the Brauer group
of a projective and geometrically integral k-rational curve (with arbitrary
singularities) over any field k. We also extend a well-known theorem of
Roquette and Lichtenbaum to a class of singular curves over any local field.
