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Computation Data

Algebraic surfaces

• Zariski pairs on cubic surfaces
• Mordell-Weil groups and automorphism groups of elliptic K3 surfaces
• Automorphism groups of certain Enriques surfaces(joint work with Simon Brandhorst)
• On characteristic polynomials of automorphisms of Enriques surfaces (joint work with Simon Brandhorst and Sławomir Rams)
• A note on configurations of (-2)-vectors on Enriques surfaces
• 15-nodal quartic surfaces. Part II: The automorphism group (joint work with Igor Dolgachev)
• Borcherds' method for Enriques surfaces (joint work with Simon Brandhorst)
• Enriques involutions on singular K3 surfaces of small discriminants (joint work with Davide Cesare Veniani)
• The elliptic modular surface of level 4 and its reduction modulo 3
• Rational double points on Enriques surfaces
• A note on Mirand-Morrison theory
• On an Enriques surface associated with a quartic Hessian surface
• Connected components of the moduli of elliptic K3 surfaces
• On a smooth quartic surface containing 56 lines which is isomorphic as a K3 surface to the Fermat quartic (joint work with Tetsuji Shioda)
• Automorphisms of supersingular K3 surfaces and Salem polynomials
• An algorithm to compute automorphism groups of K3 surfaces and an application to singular K3 surfaces
• The automorphism groups of certain singular K3 surfaces and an Enriques surface
• Dynkin diagrams of rank 20 on supersingular K3 surfaces (joint work with De Qi Zhang)
• On the supersingular K3 surface in characteristic 5 with Artin invariant 1 (joint work with T. Katsura and S. Kondo)
• Automorphism group of a supersingular K3 surface with Artin invariant 1 in characteristic 3 (joint work with S. Kondo)
• On elliptic K3 surfaces
• Rational double points on supersingular K3 surfaces

Lattices, Codes, and Graphs

• A note on construction of the Leech lattice
• A note on Quebbemann's extremal lattices of rank 64
• An even extremal lattice of rank 64
• On Edge's correspondence associated with $\cdot 222$
• The list of holes of the Leech lattice
• The graphs of Hoffman-Singleton, Higman-Sims, McLaughlin, and the Hermitian curve of degree 6 in characteristic 5

Zariski pairs on cubic surfaces

Paper: pdf

Explanation of the data: pdf

The computational data: ZPcubic.txt (682KB)

Mordell-Weil groups and automorphism groups of elliptic K3 surfaces

Paper: pdf

Explanation of the data: pdf

The computational data: CompDataXfg.txt (18.6MB)

Automorphism groups of certain Enriques surfaces (joint work with Simon Brandhorst)

Paper: pdf

Full table of elliptic fibrations: pdf

Explanation of the data: pdf

The computational data: compdata.zip (107.3MB)

On characteristic polynomials of automorphisms of Enriques surfaces (joint work with Simon Brandhorst and Sławomir Rams)

Paper: pdf

Explanation of the data: pdf

The computational data:
autYrec1.txt
autYrec2.txt
autYrec3.txt

A note on configurations of (-2)-vectors on Enriques surfaces

Paper: pdf

Explanation of the data: pdf

The computational data: L10L26compdata2.txt

15-nodal quartic surfaces. Part II: The automorphism group (joint work with Igor Dolgachev)

Paper: pdf

Explanation of the data: pdf

The computational data: 15nodalcompdata.txt

Borcherds' method for Enriques surfaces (joint work with Simon Brandhorst)

Paper: pdf

Explanation of the data: pdf

The computational data: L10L26compdata.txt

Enriques involutions on singular K3 surfaces of small discriminants (joint work with Davide Cesare Veniani)

Paper: pdf

Explanation of the data: pdf

The computational data:
NKrecs.txt
Xd3a2b1c2.txt
Xd4a2b0c2.txt
Xd7a2b1c4.txt
Xd8a2b0c4.txt
Xd12a2b0c6.txt
Xd12a4b2c4.txt
Xd15a2b1c8.txt
Xd16a4b0c4.txt
Xd20a4b2c6.txt
Xd24a2b0c12.txt
Xd36a6b0c6.txt

zipped file (18.4MB)

The table of lattices M^{144}_{10,3}, ... N^{0,274}_{10,2048} in Section 3 of the paper. latticetable.pdf (41KB)

The elliptic modular surface of level 4 and its reduction modulo 3

Paper: pdf

Explanation of the data: pdf

The computational data:
S0S3.txt
PGU.txt
Borcherds.txt
Enriques.txt

zipped file (21MB)

Rational double points on Enriques surfaces

Paper: pdf

Explanation of the data: pdf

The computational data:
discADE.txt
EmbsList.txt
Embs.txt
GramADE.txt
GramL10.txt
PhisList.txt
Phis.txt
SigmasList.txt
Sigmas.txt
Table.txt

zipped file of the folder RDPEnriquesFolder (1.1MB)

A note on Mirand-Morrison theory: pdf

This note presents a simple part of the computations for the connected components of the moduli of elliptic K3 surfaces.

On an Enriques surface associated with a quartic Hessian surface

Paper: pdf

Explanation of the data: pdf

The computational data: zipped text (36MB) : zipped folder (37MB)

Connected components of the moduli of elliptic K3 surfaces

Paper: pdf

Explanation of the data: pdf

The computational data: text

A note on Mirand-Morrison theory (a simple part of the computation): pdf

On a smooth quartic surface containing 56 lines which is isomorphic as a K3 surface to the Fermat quartic (joint work with Tetsuji Shioda)

Paper: pdf

Explanation of the data: pdf

The computational data: text

Automorphisms of supersingular K3 surfaces and Salem polynomials

Paper: Automorphisms of supersingular K3 surfaces and Salem polynomials pdf

Explanation of the data: pdf

The computational data:
compdataIS0.txt datas for p<100 (18 MB)
sigma10IS17.txt datas for 17000< p<=17389 and sigma=10 (2.6 MB)
compdataIS.zip zip file (Removed from the disc. Available upon request)

An algorithm to compute automorphism groups of K3 surfaces and an application to singular K3 surfaces

Paper: pdf

Automorphism groups of complex elliptic K3 surfaces with Picard number 3 (27 pages. This is an extended version of Section 9 of the paper.) pdf .

Automorphism groups of three singular K3 surfaces: Explanation of the data. pdf

The zip file of the three files: disc11.txt, disc15.txt, disc16.txt zip (32 MB)

The automorphism groups of certain singular K3 surfaces and an Enriques surface

Paper: pdf

The automorphism groups of certain singular K3 surfaces and an Enriques surface: computational data. pdf

GramS.txt
ample.txt
AutXa.txt
walls.txt
Invols.txt
EnriquesInvol.txt
NonSympOrder4.txt
hrhodata.txt
SympInvol14.txt
hsigmadata.txt
threeinvols_AutXa.txt
adjacentAutX.txt
Isom.txt
GramL.txt
w0.txt
EmbS.txt
EmbR.txt
EmbZ.txt
GramSZ.txt
prZMat.txt
gensAutZ.txt
DZ0.txt

The zip file zip (0.8MB)

Dynkin diagrams of rank 20 on supersingular K3 surfaces (joint work with De Qi Zhang)

The complete list of R-supersingular K3 primes for Dynkin diagrams R of rank 20.

Download of the data:

Paper: pdf (Explanation of the algorithm and the table of the list typeset by TeX. 45 pages)

List: txt (The table of R-supersingular K3 primes in Maple format)

On the supersingular K3 surface in characteristic 5 with Artin invariant 1 (joint work with T. Katsura and S. Kondo)

Paper: pdf

Explanation of the data: "Supersingular K3 surface in characteristic 5: computational data" pdf

compdataB: txt (file size: 2.4 KB)
compdataChams: txt (file size: 7.8 MB)
compdataKm: txt (file size: 1.6 KB)

Automorphism group of a supersingular K3 surface with Artin invariant 1 in characteristic 3 (joint work with S. Kondo)

We present a finite set of generators of the autmorphism group of a supersingular K3 surface with Arin invariant 1 in characteristic 3.

Paper: pdf

Explanation of the data: Computational data of the paper "The automorphism group of a supersingular K3 surface with Artin variant 1 in characteristic 3" pdf

compdataAutFQChar3: txt (file size: 1.1 MB)
FQprojautfolder.tar.gz: tar.gz of the FQprojaut and FQprojautS (file size: 274 MB)

On elliptic K3 surfaces

The list of pairs of the ADE-type of singular fibers and the torsion of Modell-Weil groups of complex elliptic K3 surfaces

Download of the data:

Paper: pdf (Explanation of the algorithm. Certain properties of the list are also presented.)

Paper: pdf (110 pages)

Table: pdf (The table of the list typeset by TeX. 36 pages.)

List: text (The list of all 3693 pairs in plain text format.)

Rational double points on supersingular K3 surfaces

The complete list of configurations of rational double points with the total Milnor number 21 on supersingular K3 surfaces is given.
We also presents the complete list of extremal (quasi-)elliptic fibrations on supersingular K3 surfaces.

Download of the data:

Paper: pdf (Explanation of the algorithm and the table of the list typeset by TeX. 31 pages)

List: RDP.txt (The list of geometrically realizable RDP triples in Maple format)

List: Elliptic.txt (The list of geometrically realizable elliptic triples in Maple format)

A note on construction of the Leech lattice

Paper: A note on construction of the Leech lattice: pdf

Explanation of the data: Computational data for the paper ``A note on constructions of the Leech lattice": pdf

The computational data: ConstructionsLeech.txt (1.9 MB)

A note on Quebbemann's extremal lattices of rank 64

Paper: A note on Quebbemann's extremal lattices of rank 64: pdf

Explanation of the data: A note on Quebbemann's extremal lattices of rank 64: Computation data: pdf

The computational data: zipped folder compdataQuebbemann.zip (582 MB)

An even extremal lattice of rank 64

Paper: An even extremal lattice of rank 64: pdf

Explanation of the data: An even extremal lattice of rank 64: computational data: pdf

The computational data:
zipped folder compdataL64 (354.3 MB)

On Edge's correspondence associated with $\cdot 222$

Paper: On Edge's correspondence associated with $\cdot 222$: pdf

Explanation of the data: On Edge's correspondence associated with $\cdot 222$: computational data: pdf

The computational data: text file (458 KB)

The list of holes of the Leech lattice

Paper: Holes of the Leech lattice and the projective models of K3 surfaces: pdf

A note on the enumeration of holes of Leech lattice (Appendix A of the preprint above): pdf

Explanation of the data (new version, Appendix B of the preprint above): pdf

The computational data (new version in GAP format): text file (770 KB)

Below is the old version of the computational data in Maple format

Explanation of the data (old version): pdf

The computational data (old version in Maple format): text file (770 KB)

The graphs of Hoffman-Singleton, Higman-Sims, McLaughlin, and the Hermitian curve of degree 6 in characteristic 5

Paper: The graphs of Hoffman-Singleton, Higman-Sims, McLaughlin, and the Hermitian curve of degree 6 in characteristic 5: pdf

Explanation of the data: pdf

The zip file: compdataHS.zip

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