A $1$-dimensional family of Enriques surfaces in characteristic $2$ covered by the supersingular $K3$ surface with Artin invariant $1$

Katsura, Takeshi; Kondō, Shigeyuki

doi:10.4310/pamq.2015.v11.n4.a6

Cited by 7 publications

(2 citation statements)

References 19 publications

(29 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using Tables [10, p.9 and pp. [16][17][18], we easily see that the left-most vertex in Figure 20 is part of the conductrix and hence, by Lemma 3.3 and Proposition 2.8, it is the curve of cusps of the two quasi-elliptic fibrations of type (II * ). Then, similarly, Table 6 shows that the Ẽ7 diagram is a double fiber of a quasi-elliptic fibration of type (2III * , III), which is the fibration induced by π.…”

Section: Figure 21mentioning

confidence: 96%

Classification of Enriques surfaces with finite automorphism group in characteristic 2

Katsura¹,

Kondō²,

Martin³

2017

Preprint

Self Cite

View full text Add to dashboard Cite

We classify supersingular and classical Enriques surfaces with finite automorphism group in characteristic 2 into 8 types according to their dual graphs of all (−2)curves (nonsigular rational curves). We give examples of these Enriques surfaces together with their canonical coverings. It follows that the classification of all Enriques surfaces with finite automorphism group in any characteristics has been finished.(2) §12 Enriques surfaces of type D8 §13 Enriques surfaces of type D4 + D4 §14 Appendix2010 Mathematics Subject Classification. 14J28 (primary), 14J50, 14G17 (secondary).

show abstract

Section: Figure 21mentioning

confidence: 96%

Classification of Enriques surfaces with finite automorphism group in characteristic 2

Katsura¹,

Kondō²,

Martin³

2017

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The goal of this paper is to analyze the structure of K3-like coverings X, and the ensuing simply connected Enriques surfaces Y . These where already investigated, among others, by Bombieri and Mumford [6], Blass [4], Lang [27,28], Cossec and Dolgachev [11], Ekedahl and Shepherd-Barron [15] in the non-normal case, Ekedahl, Hyland and Shepherd Barron [16] in the normal case, Katsura and Kondo [25], and Liedtke [32]. There are, however, many open foundational questions.…”

mentioning

confidence: 99%

Enriques surfaces with normal K3-like coverings

Schröer¹

2017

Preprint

View full text Add to dashboard Cite

We analyze the structure of simply-connected Enriques surface in characteristic two whose K3-like covering is normal, building on the work of Ekedahl, Hyland and Shepherd-Barron. We develop general methods to construct such surfaces and the resulting twistor lines in the moduli stack of Enriques surfaces, including the case that the K3-like covering is a normal rational surface rather then a normal K3 surface. Among other things, we show that elliptic double points indeed do occur. In this case, there is only one singularity. The main idea is to apply flops to Frobenius pullbacks of rational elliptic surfaces, to get the desired K3-like covering. Our results hinge on Lang's classification of rational elliptic surfaces, the determination of their Mordell-Weil lattices by Shioda and Oguiso, and the behavior of unstable fibers under Frobenius pullback via Ogg's Formula. Along the way, we develop a general theory of Zariski singularities in arbitrary dimension, which is tightly interwoven with the theory of height-one group schemes actions and restricted Lie algebras. Furthermore, we determine under what conditions tangent sheaves are locally free, and introduce a theory of canonical coverings for arbitrary proper algebraic schemes.

show abstract

Enriques surfaces in characteristic 2 with a finite group of automorphisms

Katsura

Kondō

2017

J. Algebraic Geom.

View full text Add to dashboard Cite

Complex Enriques surfaces with a finite group of automorphisms are classified into seven types. In this paper, we determine which types of such Enriques surfaces exist in characteristic 2. In particular we give a 1-dimensional family of classical and supersingular Enriques surfaces with the automorphism group A u t ( X ) \mathrm {Aut}(X) isomorphic to the symmetric group S 5 \mathfrak {S}_5 of degree 5.

show abstract

A $1$-dimensional family of Enriques surfaces in characteristic $2$ covered by the supersingular $K3$ surface with Artin invariant $1$

Cited by 7 publications

References 19 publications

Classification of Enriques surfaces with finite automorphism group in characteristic 2

Classification of Enriques surfaces with finite automorphism group in characteristic 2

Enriques surfaces with normal K3-like coverings

Enriques surfaces in characteristic 2 with a finite group of automorphisms

Contact Info

Product

Resources

About