A relative GAGA principle for families of curves

Jack Hall

doi:10.1112/jlms/jdu012

A relative GAGA principle for families of curves

Jack Hall^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We prove a relative GAGA principle for families of curves, showing: (i) analytic families of pointed curves whose fibres have finite automorphism groups are algebraizable; and (ii) analytic birational models of \mathcal {M}-{g,n} possessing modular interpretations with the finite automorphism property are algebraizable. This is accomplished by extending some well-known GAGA results for proper schemes to non-separated Deligne-Mumford stacks.

Original language	English
Pages (from-to)	29-48
Number of pages	20
Journal	Journal of the London Mathematical Society
Volume	90
Issue number	1
DOIs	https://doi.org/10.1112/jlms/jdu012
Publication status	Published - Aug 2014

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abstract = "We prove a relative GAGA principle for families of curves, showing: (i) analytic families of pointed curves whose fibres have finite automorphism groups are algebraizable; and (ii) analytic birational models of \mathcal {M}-{g,n} possessing modular interpretations with the finite automorphism property are algebraizable. This is accomplished by extending some well-known GAGA results for proper schemes to non-separated Deligne-Mumford stacks.",

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AB - We prove a relative GAGA principle for families of curves, showing: (i) analytic families of pointed curves whose fibres have finite automorphism groups are algebraizable; and (ii) analytic birational models of \mathcal {M}-{g,n} possessing modular interpretations with the finite automorphism property are algebraizable. This is accomplished by extending some well-known GAGA results for proper schemes to non-separated Deligne-Mumford stacks.

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JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

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A relative GAGA principle for families of curves

Abstract

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