Macaulay2 package K3Carpets -- The unique Gorenstein double structure on a surface scroll. This package accompanies our paper Equations and syzygies of K3 carpets and union of scrolls for experimental exploration: Equations and Syzygies of K3 Carpets and Unions of Scrolls. We describe the equations and Gröbner bases of some degenerate K3 surfaces associated to rational normal scrolls. These K3 surfaces are members of a class of interesting singular projective varieties we call correspondence scrolls. The ideals of these surfaces are nested in a simple way that allows us to analyze them inductively. We describe explicit Gröbner bases and syzygies for these objects over the integers and this lets us treat them in all characteristics simultaneously.
Keywords for this software
References in zbMATH (referenced in 5 articles , 1 standard article )
Showing results 1 to 5 of 5.
- Aprodu, Marian; Farkas, Gavril; Papadima, Ştefan; Raicu, Claudiu; Weyman, Jerzy: Koszul modules and Green’s conjecture (2019)
- Brake, Danielle A.; Hauenstein, Jonathan D.; Schreyer, Frank-Olaf; Sommese, Andrew J.; Stillman, Michael E.: Singular value decomposition of complexes (2019)
- Eisenbud, David; Sammartano, Alessio: Correspondence scrolls (2019)
- Eisenbud, David; Schreyer, Frank-Olaf: Equations and syzygies of (K3) carpets and unions of scrolls (2019)
- David Eisenbud, Frank-Olaf Schreyer: Equations and Syzygies of K3 Carpets and Unions of Scrolls (2018) arXiv