# 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} }

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:

#### Figures from this paper

#### 4 Citations

Normal quintic surfaces with Kodaira dimension one

- Mathematics
- 2015

We study normal quintic surfaces in the three-dimensional projective space whose nonsingular models are surfaces of Kodaira dimension one. It turns out that the genus of the base curve of their… Expand

Brill–Noether theory of curves on Enriques surfaces I: the positive cone and gonality

- Mathematics
- 2008

We study the existence of linear series on curves lying on an Enriques surface and general in their complete linear system. Using a method that works also below the Bogomolov–Reider range, we… Expand

Brill–Noether theory of curves on Enriques surfaces II: the Clifford index

- Mathematics
- 2013

We complete our study of linear series on curves lying on an Enriques surface by showing that, with the exception of smooth plane quintics, there are no exceptional curves on Enriques surfaces, that… Expand

A brief introduction to Enriques surfaces

- Mathematics
- 2014

This is a brief introduction to the theory of Enriques surfaces over arbitrary algebraically closed fields. Some new results about automorphism groups of Enriques surfaces are also included.

#### References

SHOWING 1-10 OF 24 REFERENCES

Smooth rational curves on Enriques surfaces

- Mathematics
- 1985

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 is… Expand

On the Picard group of Enriques surfaces

- Mathematics
- 1985

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 defined… Expand

Automorphisms of Enriques surfaces

- Mathematics
- 1983

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 for… Expand

On Self-Intersection Number of a Section on a Ruled Surface

- Mathematics
- 1970

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 a… Expand

ON ISOLATED RATIONAL SINGULARITIES OF SURFACES.

- Mathematics
- 1966

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). These… Expand

On normal quintic Enriques surfaces.

- Mathematics
- 1991

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 two… Expand

The rationality of the moduli space of Enriques surfaces

- Mathematics
- 1994

An arrangement for mounting one end of a piezoelectric element operating in a bending mode about the one end to generate essentially linear movement for a part of a moving component operatively… Expand

Über die Auflösung gewisser Singularitäten von holomorphen Abbildungen

- Mathematics, Materials Science
- 1966

A windshield wiper blade liner made from a substantially non-wettable synthetic polymeric material which is pre-stressed to snap onto a wiper blade. The liner is formed with a V-shaped wiper section… Expand