On the Severi problem in arbitrary characteristic

Karl Christ, Xiang He, Ilya Tyomkin

Research output: Working paper/PreprintPreprint

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We show that Severi varieties parametrizing irreducible reduced planar curves of given degree and geometric genus are either empty or irreducible in any characteristic. As a consequence, we generalize Zariski's theorem to positive characteristic and show that a general reduced planar curve of given geometric genus is nodal. As a byproduct, we obtain the first proof of the irreducibility of the moduli space of smooth projective curves of given genus in positive characteristic, that does not involve a reduction to the characteristic zero case.
Original languageEnglish GB
PublisherarXiv:2005.04134 [math.AG]
StatePublished - 2020


  • math.AG
  • 14D20, 14H10, 14H50, 14T05


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