Description
This package contains code and examples for the paper [QQ] Quaternary Quartic Forms and Gorenstein Rings, by Grzegorz Kapustka, Michal Kapustka, Kristian Ranestad, Hal Schenck, Mike Stillman and Beihui Yuan, referenced below.
We study the space of quartic forms in four variables, interleaving the notions of: rank, border rank, annihilator of the quartic form, Betti tables, and CalabiYau varieties of codimension 4.
Section 1: Generating the Betti tables
Section 2: Basic constructions
Section 3: betti tables for points in P^3 with given geometry
Section 4: the quadratic part of the apolar ideal
Section 5: VSP(F,9) for a general quadric form of rank 9

VSP(F_Q,9)  Computation appearing in the proof of Theorem 5.16 in [QQ]
Section 6: Stratification of the space of quaternary quartics
Section 7: Codimension three varieties in quadrics

Pfaffians on quadrics  compute the quartic and betti table corresponding to a pfaffian ideal in a quadric
Section 8: Irreducible liftings
Section 9: Construction and lifting of AG varieties

Type [210], CY of degree 18 via linkage  lifting to a 3fold with components of degrees 11, 6, 1

Type [310], CY of degree 17 via linkage  lifting to a 3fold with components of degrees 11, 6

Type [331], CY of degree 17 via linkage  lifting to a 3fold with components of degrees 13 and 4

Type [420], CY of degree 16 via linkage  lifting to an irreducible 3fold

Type [430], CY of degree 16 via linkage  lifting to a 3fold with components of degrees 10, 6

Type [441a], CY of degree 16  lifting to a 3fold with components of degrees 12, 4

Type [441b], CY of degree 16  lifting to a 3fold with components of degrees 8, 8

Type [551], CY of degree 15 via linkage  lifting to a 3fold with components of degrees 11 and 4

Type [562] with lifting of type I, a CY of degree 15 via linkage  lifting to a 3fold with components of degree 8, 7

Type [562] with a lifting of type II, a CY of degree 15 via linkage  lifting to a 3fold with components of degrees 7, 4, 4
Appendix 2: Components of the Betti table loci in Hilbert schemes of points