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Moduli of algebraic varieties

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arxiv 2211.11237 v1 pith:OGDG77R3 submitted 2022-11-21 math.AG

Caucher Birkar This is my paper · ORCID
classification math.AG
keywords modulialgebraicvarietiesappliedcertaincoarseconditionsconstruct
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We develop a moduli theory of algebraic varieties and pairs of non-negative Kodaira dimension. We define stable minimal models and construct their projective coarse moduli spaces under certain natural conditions. This can be applied to a wide range of moduli problems in algebraic geometry.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Stratified Hyperbolicity of the moduli stack of stable minimal models, I

    math.AG 2025-06 conditional novelty 7.0 of 10

    Birationally admissible families of stable minimal models with maximal variation have log general type bases, yielding stratified hyperbolicity of the KSBA moduli stack.

  2. Compact moduli of elliptic surfaces with a multiple fiber

    math.AG 2025-09 conditional novelty 6.0 of 10

    New moduli stacks for marked rational elliptic surfaces of index m and a list of slc surfaces that smooth to Dolgachev surfaces when a multiple fiber degenerates.

  3. Stratified Hyperbolicity of the moduli stack of stable minimal models, II: Big Picard Theorem and the stratified Brody hyperbolicity

    math.AG 2025-06 conditional novelty 6.0 of 10

    Every stratum in a birationally admissible stratification of Birkar's moduli stack of stable minimal models is Picard hyperbolic, Borel hyperbolic, and Brody hyperbolic.

  4. Positivity, singularities, and boundedness

    math.AG 2025-07 conditional novelty 4.0 of 10

    A survey note on positivity, singularities, and boundedness in birational geometry that includes a sketchy proof of a new theorem bounding fibre multiplicities in fibrations.

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