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An analytic proof of the stable reduction theorem. | LitMetric

An analytic proof of the stable reduction theorem.

Math Ann

Department of Mathematics and Computer Science, Rutgers University, Newark, NJ 07102 USA.

Published: April 2024

AI Article Synopsis

  • - The stable reduction theorem states that for a family of curves of a specific genus over a punctured curve, you can uniquely complete them by adding stable curves at the punctures, potentially after changing the base.
  • - The authors present a new version of this theorem for curves over a particular field, focusing on using Kähler-Einstein metrics.
  • - These Kähler-Einstein metrics help in determining the stable curves that appear at the punctures in the limit.

Article Abstract

The stable reduction theorem says that a family of curves of genus over a punctured curve can be uniquely completed (after possible base change) by inserting certain stable curves at the punctures. We give a new this result for curves defined over , using the Kähler-Einstein metrics on the fibers to obtain the limiting stable curves at the punctures.

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Source
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC11561019PMC
http://dx.doi.org/10.1007/s00208-024-02848-2DOI Listing

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