Universal degeneration of Riemann surfaces and fibered complex surfaces

Tadashi Ashikaga; Yukio Matsumoto

Universal degeneration of Riemann surfaces and fibered complex surfaces

Algebraic Geometry 2023-01-03 v1 Complex Variables Geometric Topology

Authors: Tadashi Ashikaga , Yukio Matsumoto

Abstract

Based on Teichm\"uller theory, we construct a degenerating family $\overline{Y}_g^{orb} \rightarrow \overline{M}_g^{orb}$ over the Deligne-Mumford compactification of the moduli space with the natural orbifold structure such that any fibered complex surface admitting unstable fibers can be pulled back from this family.

Keywords

riemann surfaces fibered complex surfaces universal degeneration teichmuller theory deligne-mumford compactification orbifold unstable fibers

Cite

@article{arxiv.2301.00381,
  title  = {Universal degeneration of Riemann surfaces and fibered complex surfaces},
  author = {Tadashi Ashikaga and Yukio Matsumoto},
  journal= {arXiv preprint arXiv:2301.00381},
  year   = {2023}
}

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79 pages, 7 figures

Universal degeneration of Riemann surfaces and fibered complex surfaces

Abstract

Keywords

Cite

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