Quentin Posva - Abundance for slc surfaces over arbitrary fields

epiga:8803 - Épijournal de Géométrie Algébrique, February 15, 2023, Volume 7 - https://doi.org/10.46298/epiga.2023.volume7.8803
Abundance for slc surfaces over arbitrary fieldsArticle

Authors: Quentin Posva

    We prove the abundance conjecture for projective slc surfaces over arbitrary fields of positive characteristic. The proof relies on abundance for lc surfaces over abritrary fields, proved by Tanaka, and on the technique of Hacon and Xu to descend semi-ampleness from the normalization. We also present applications to dlt threefold pairs, and to mixed characteristic families of surfaces.


    Volume: Volume 7
    Published on: February 15, 2023
    Accepted on: October 23, 2022
    Submitted on: December 6, 2021
    Keywords: Mathematics - Algebraic Geometry
    Funding:
      Source : OpenAIRE Graph
    • Moduli spaces of stable varieties and applications; Funder: European Commission; Code: 804334

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