Normal quintic surfaces which are birationally Enriques surfaces

@article{Umezu1997NormalQS,
  title={Normal quintic surfaces which are birationally Enriques surfaces},
  author={Yumiko Umezu},
  journal={Publications of The Research Institute for Mathematical Sciences},
  year={1997},
  volume={33},
  pages={359-384}
}
  • Yumiko Umezu
  • Published 1997
  • Mathematics
  • Publications of The Research Institute for Mathematical Sciences
Let S be an Enriques surface over an algebraically closed field k of characteristic ^2. Then, equivalently, S is a non-singular projective surface with q(S)=pg(S) = Q and 2KS^Q. It is known (cf. Cossec [Co]) that every Enriques surface admits a morphism of degree one onto a surface of degree 10 in P with isolated rational double points, and also that every Enriques surface is birationally equivalent to a (non-normal) sextic surface in P. Then there arises the following problem: 

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References

SHOWING 1-10 OF 24 REFERENCES
Smooth rational curves on Enriques surfaces
Let S be an Enriques surface over an algebraically closed field k of arbitrary characteristic p. Recall that this means that S is a connected smooth projective surface whose canonical class isExpand
On the Picard group of Enriques surfaces
An Enriques surface over an algebraically closed field k of characteristic 4:2 is a non-singular projective surface S with H ~ (S, d~s)= H2(S, Cs)= 0 and 2Ks = 0. The unramitied double cover definedExpand
Automorphisms of Enriques surfaces
O. Introduction The aim of this note is to compute the group Aut(Y) of (biholomorphic) auto- morphisms for the general Enriques surface Y. The basic tool is the global To- relli theorem forExpand
On Self-Intersection Number of a Section on a Ruled Surface
Let E be a non-singular projective curve of genus g ≥ 0, P the projective line and let F be the surface E× P . Then it is well known that a ruled surface F* which is birational to F is biregular to aExpand
ON ISOLATED RATIONAL SINGULARITIES OF SURFACES.
In 1934, DuVal [3] listed the configurations of curves which can be obtained by resolving certain isolated double points of embedded surfaces (they are depicted in the figure below). TheseExpand
On normal quintic Enriques surfaces.
In this paper we describe normal quintic surfaces in P which are birationally isomorphic to Enriques surfaces. especially we characterize the sublinear systems which give rise to one of twoExpand
The rationality of the moduli space of Enriques surfaces
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Über die Auflösung gewisser Singularitäten von holomorphen Abbildungen
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