We prove that an Enriques surface S with certain configuration of half pencils is birationally equivalent to a normal quintic surface. No Enriques surfaces are known which do not satisfy this condition. We construct birational maps explicitly, and obtain the defining equations with ten parameters of the image in P3.
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Jagiellonian Univ, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow, PolandJagiellonian Univ, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow, Poland
Dumnicki, Marcin
Harbourne, Brian
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Univ Nebraska, Dept Math, Lincoln, NE 68588 USAJagiellonian Univ, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow, Poland
Harbourne, Brian
Roe, Joaquim
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Univ Autonoma Barcelona, Barcelona Grad Sch Math, Barcelona 08193, Spain
Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, SpainJagiellonian Univ, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow, Poland
Roe, Joaquim
Szemberg, Tomasz
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Pedag Univ Cracow, Dept Math, PL-30084 Krakow, PolandJagiellonian Univ, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow, Poland
Szemberg, Tomasz
Tutaj-Gasinska, Halszka
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Jagiellonian Univ, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow, PolandJagiellonian Univ, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow, Poland