Admissible Hermitian metrics on families of line bundles over certain degenerating Riemann surfaces

Wing Keung To, Lin Weng

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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 admits a nice (resp. almost nice) family of flat 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) nice family of p-singular Hermitian metrics which are admissible with respect to the canonical/hyperbolic (1,1)-forms on the Riemann surfaces.

Original languageEnglish
Pages (from-to)441-489
Number of pages49
JournalPacific Journal of Mathematics
Volume197
Issue number2
DOIs
Publication statusPublished - Jan 1 2001
Externally publishedYes

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Line Bundle
Riemann Surface
Metric
Family
Necessary Conditions
Sufficient Conditions
Zero
Vertex of a graph

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Admissible Hermitian metrics on families of line bundles over certain degenerating Riemann surfaces. / To, Wing Keung; Weng, Lin.

In: Pacific Journal of Mathematics, Vol. 197, No. 2, 01.01.2001, p. 441-489.

Research output: Contribution to journalArticle

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