Geodesic
Abundance for slc surfaces over arbitrary fields
Épijournal de Géométrie Algébrique, Tome 7 (2023)

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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. 
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     author = {Posva, Quentin},
     title = {Abundance for slc surfaces over arbitrary fields},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
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     volume = {7},
     year = {2023},
     doi = {10.46298/epiga.2023.volume7.8803},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2023.volume7.8803/}
}
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Posva, Quentin. Abundance for slc surfaces over arbitrary fields. Épijournal de Géométrie Algébrique, Tome 7 (2023). doi: 10.46298/epiga.2023.volume7.8803

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