K3Surfaces -- A package for constructing explicit examples of K3 surfaces

References

M. H. and G. S., Explicit constructions of K3 surfaces and unirational Noether-Lefschetz divisors, available at arXiv:2110.15819 (2021).

Authors

Michael Hoff <[email protected]>
Giovanni Staglianò <[email protected]>

Version

This documentation describes version 1.1 of K3Surfaces.

Source code

The source code from which this documentation is derived is in the file K3Surfaces.m2.

Exports

Types
- EmbeddedK3surface -- the class of all embedded K3 surfaces
- LatticePolarizedK3surface -- the class of all lattice-polarized K3 surfaces
Functions and commands
- K3 -- make a lattice-polarized K3 surface
- mukaiModel -- Mukai models
- pentagonalK3 -- pentagonal K3 surface
- project -- project a K3 surface
- tetragonalK3 -- tetragonal K3 surface
- trigonalK3 -- trigonal K3 surface
Methods
- coefficientRing(LatticePolarizedK3surface) -- coefficient ring of a K3 surface
- "degree(EmbeddedK3surface,ZZ,ZZ)" -- see degree(LatticePolarizedK3surface,ZZ,ZZ) -- degree of a K3 surface
- degree(LatticePolarizedK3surface,ZZ,ZZ) -- degree of a K3 surface
- "genus(EmbeddedK3surface,ZZ,ZZ)" -- see genus(LatticePolarizedK3surface,ZZ,ZZ) -- genus of a K3 surface
- genus(LatticePolarizedK3surface,ZZ,ZZ) -- genus of a K3 surface
- "K3(ZZ,ZZ,ZZ)" -- see K3 -- make a lattice-polarized K3 surface
- K3(EmbeddedK3surface) -- make a lattice-polarized K3 surface from an embedded K3 surface
- K3(SpecialCubicFourfold) -- K3 surface associated to a cubic or GM fourfold
- "K3(SpecialGushelMukaiFourfold)" -- see K3(SpecialCubicFourfold) -- K3 surface associated to a cubic or GM fourfold
- K3(String) -- show available functions to construct K3 surfaces of given genus
- K3(ZZ) -- make a general K3 surface
- "EmbeddedK3surface Sequence" -- see LatticePolarizedK3surface Sequence -- image of the embedding of a K3 surface
- LatticePolarizedK3surface Sequence -- image of the embedding of a K3 surface
- "map(EmbeddedK3surface,ZZ,ZZ)" -- see map(LatticePolarizedK3surface,ZZ,ZZ) -- embedding of a K3 surface
- map(LatticePolarizedK3surface,ZZ,ZZ) -- embedding of a K3 surface
- "mukaiModel(ZZ)" -- see mukaiModel -- Mukai models
- "pentagonalK3(ZZ)" -- see pentagonalK3 -- pentagonal K3 surface
- "project(VisibleList,EmbeddedK3surface)" -- see project -- project a K3 surface
- "project(VisibleList,LatticePolarizedK3surface,ZZ,ZZ)" -- see project -- project a K3 surface
- "tetragonalK3(ZZ)" -- see tetragonalK3 -- tetragonal K3 surface
- "trigonalK3(ZZ)" -- see trigonalK3 -- trigonal K3 surface

For the programmer

The object K3Surfaces is a package.