Augmented Teichmüller spaces and orbifolds

Vladimir Hinich, Arkady Vaintrob

Research output: Contribution to journalArticlepeer-review

Abstract

We study complex analytic properties of the augmented Teichmüller spaces T̄g,n obtained by adding to the classical Teichmüller spaces Tg,n points corresponding to Riemann surfaces with nodal singularities. Unlike Tg,n, the space T̄g,n is not a complex manifold (it is not even locally compact). We prove, however, that the quotient of the augmented Teichmüller space by any finite index subgroup of the Teichmüller modular group has a canonical structure of a complex orbifold. Using this structure, we construct natural maps from T̄ to stacks of admissible coverings of stable Riemann surfaces. This result is important for understanding the cup-product in stringy orbifold cohomology. We also establish some new technical results from the general theory of orbifolds which may be of independent interest.

Original languageEnglish
Pages (from-to)533-629
Number of pages97
JournalSelecta Mathematica, New Series
Volume16
Issue number3
DOIs
StatePublished - 2010

Bibliographical note

Funding Information:
The work of the second author was partially supported by the NSF grant DMS-0407000.

ASJC Scopus subject areas

  • Mathematics (all)
  • Physics and Astronomy (all)

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