Wk. To et L. Weng, Admissible Hermitian metrics on families of line bundles over certain degenerating Riemann surfaces, PAC J MATH, 197(2), 2001, pp. 441-489
We show that a family of line bundles of degree zero over a plumbing family
of Riemann surfaces with a separating ( resp. non-separating) node p admit
s a nice ( resp. almost nice) family of at p-singular Hermitian metrics. As
a consequence, we give necessary and sufficient conditions for a family of
line bundles over such families of Riemann surfaces to admit an (almost) n
ice family of p-singular Hermitian metrics which are admissible with respec
t to the canonical/hyperbolic (1,1)-forms on the Riemann surfaces.