Miyanishi, Masayoshi Unirational quasi-elliptic surfaces in characteristic 3. (English) Zbl 0358.14019 Osaka J. Math. 13, 513-522 (1976). A non-singular projective surface is called “quasi-elliptic”; if it admits a morphism \(f\) to a curve \(C\), where almost all the fibres of \(f\) are irreducible singular rational curves of arithmetic genus one. By a theorem of Tate such a surface can exist only in the rase where the characteristic of the groundfieldis 2 or 3. The author considers the rase of a quasi-elliptic surface \(X\) of characteristic 3 for which \(f\) admits a rational section, and \(X\) is unirational (equivalently: \(C\) is rational). He computes some of the basic invariants of there surfaces, under further hypotheses. Reviewer: Barry Mazur Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 Documents MSC: 14J15 Moduli, classification: analytic theory; relations with modular forms 14M20 Rational and unirational varieties 14G15 Finite ground fields in algebraic geometry PDF BibTeX XML Cite \textit{M. Miyanishi}, Osaka J. Math. 13, 513--522 (1976; Zbl 0358.14019) OpenURL