K3Surfaces -- construction of explicit examples of K3 surfaces

Description

This package is 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.