In mathematics, a Raynaud surface is a particular kind of algebraic surface that was introduced in William E. Lang (1979) and named for Michel Raynaud (1978). To be precise, a Raynaud surface is a quasi-elliptic surface over an algebraic curve of genus g greater than 1, such that all fibers are irreducible and the fibration has a section. The Kodaira vanishing theorem fails for such surfaces; in other words the Kodaira theorem, valid in algebraic geometry over the complex numbers, has such surfaces as counterexamples, and these can only exist in characteristic p.
Generalized Raynaud surfaces were introduced in (Lang 1983), and give examples of surfaces of general type with global vector fields.
References
- Lang, William E. (1979), "Quasi-elliptic surfaces in characteristic three", Annales Scientifiques de l'École Normale Supérieure, Série 4, 12 (4): 473–500, ISSN 0012-9593, MR 0565468
- Lang, William E. (1983), "Examples of surfaces of general type with vector fields", Arithmetic and geometry, Vol. II, Progress in Mathematics, vol. 36, Boston, MA: Birkhäuser Boston, pp. 167–173, MR 0717611
- Raynaud, Michel (1978), "Contre-exemple au "vanishing theorem" en caractéristique ", C. P. Ramanujam—a tribute, Tata Inst. Fund. Res. Studies in Math., vol. 8, Berlin, New York: Springer-Verlag, pp. 273–278, MR 0541027
🔥 Top keywords: Main PageSpecial:SearchPage 3Wikipedia:Featured picturesHouse of the DragonUEFA Euro 2024Bryson DeChambeauJuneteenthInside Out 2Eid al-AdhaCleopatraDeaths in 2024Merrily We Roll Along (musical)Jonathan GroffJude Bellingham.xxx77th Tony AwardsBridgertonGary PlauchéKylian MbappéDaniel RadcliffeUEFA European Championship2024 ICC Men's T20 World CupUnit 731The Boys (TV series)Rory McIlroyN'Golo KantéUEFA Euro 2020YouTubeRomelu LukakuOpinion polling for the 2024 United Kingdom general electionThe Boys season 4Romania national football teamNicola CoughlanStereophonic (play)Gene WilderErin DarkeAntoine GriezmannProject 2025