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QuaternaryQuartics : Index
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[QQ]
-- Quaternary Quartic Forms and Gorenstein rings (Kapustka, Kapustka, Ranestad, Schenck, Stillman, Yuan, 2021)
bettiStrataExamples
-- a hash table consisting of examples for each of the 19 Betti strata
bettiStrataExamples(Ring)
-- a hash table consisting of examples for each of the 19 Betti strata
Computation of a doubling for each Betti table type
-- See Proposition 2.18 in [QQ]
Count
-- an option name
doubling
-- implement the doubling construction
Doubling Examples
-- Doubling of each type of set of points
Doubling Examples for ideals of 6 points
-- For an ideal $I_{\Gamma}$ of six points we compute possible doublings of $I_{\Gamma}$. See Example 2.16 in [QQ] for details
doubling(...,Count=>...)
-- implement the doubling construction
doubling(ZZ,Ideal)
-- implement the doubling construction
Example Type [300a]
-- An example of an apolar ideal of a quartic that cannot be obtained as a doubling of it's apolar set
Example Type [300b]
-- An example of doubling construction
Example Type [300c]
-- The third family of type [300]
Finding all possible betti tables for quadratic component of inverse system for quartics in 4 variables
-- Material from Section 4 of [QQ]
Finding the 16 betti tables possible for quartic forms in 4 variables, and examples
-- Material from Table 6 and 7 of Appendix 1
Finding the Betti stratum of a given quartic
-- the 19 Betti strata
Finding the possible betti tables for points in P^3 with given geometry
-- Material from Section 3 of [QQ]
Half canonical degree 20
-- Computation which supports the proof of Proposition 8.4
Hilbert scheme of 6 points in projective 3-space
-- Betti table loci
Noether-Lefschetz examples
-- examples from Section 6.2 in [QQ]
nondegenerateBorels
-- construct all nondegenerate strongly stable ideals of given length
nondegenerateBorels(...,Sort=>...)
-- construct all nondegenerate strongly stable ideals of given length
nondegenerateBorels(ZZ,Ring)
-- construct all nondegenerate strongly stable ideals of given length
Normalize
-- an option name
Pfaffians on quadrics
-- compute the quartic and betti table corresponding to a pfaffian ideal in a quadric
pointsIdeal
-- create an ideal of points
pointsIdeal(Matrix)
-- create an ideal of points
pointsIdeal(Ring,Matrix)
-- create an ideal of points
quartic
-- a quartic given by power sums of linear forms
quartic(Matrix)
-- a quartic given by power sums of linear forms
quartic(Matrix,Ring)
-- a quartic given by power sums of linear forms
quarticType
-- the Betti stratum a specific quartic lies on
quarticType(RingElement)
-- the Betti stratum a specific quartic lies on
QuaternaryQuartics
-- code to support the paper 'Quaternary Quartic Forms and Gorenstein Rings'
random(List,Ideal)
-- a random ring element of a given degree
random(ZZ,Ideal)
-- a random ring element of a given degree
randomBlockMatrix
-- create a block matrix with zero, identity and random blocks
randomBlockMatrix(List,List,List)
-- create a block matrix with zero, identity and random blocks
randomHomomorphism
-- create a random homomorphism between graded modules
randomHomomorphism(List,Module,Module)
-- create a random homomorphism between graded modules
randomHomomorphism(ZZ,Module,Module)
-- create a random homomorphism between graded modules
randomPoints
-- create a matrix whose columns are random points
randomPoints(...,Normalize=>...)
-- create a matrix whose columns are random points
randomPoints(Ring,ZZ)
-- create a matrix whose columns are random points
randomPoints(Ring,ZZ,ZZ)
-- create a matrix whose columns are random points
Singularities of lifting of type [300b]
-- The lifting of [300b] defined by biliaison acquires singularities in dimension 3
smallerBettiTables
-- Find all (potentially) smaller Betti tables that could degenerate to given table
smallerBettiTables(BettiTally)
-- Find all (potentially) smaller Betti tables that could degenerate to given table
Type [000], CY of degree 20
-- lifting to a 3-fold with two singular points
Type [210], CY of degree 18 via linkage
-- lifting to a 3-fold with components of degrees 11, 6, 1
Type [310], CY of degree 17 via linkage
-- lifting to a 3-fold with components of degrees 11, 6
Type [331], CY of degree 17 via linkage
-- lifting to a 3-fold with components of degrees 13 and 4
Type [420], CY of degree 16 via linkage
-- lifting to an irreducible 3-fold
Type [430], CY of degree 16 via linkage
-- lifting to a 3-fold with components of degrees 10, 6
Type [441a], CY of degree 16
-- lifting to a 3-fold with components of degrees 12, 4
Type [441b], CY of degree 16
-- lifting to a 3-fold with components of degrees 8, 8
Type [551], CY of degree 15 via linkage
-- lifting to a 3-fold with components of degrees 11 and 4
Type [562] with a lifting of type II, a CY of degree 15 via linkage
-- lifting to a 3-fold with components of degrees 7, 4, 4
Type [562] with lifting of type I, a CY of degree 15 via linkage
-- lifting to a 3-fold with components of degree 8, 7
VSP(F_Q,9)
-- Computation appearing in the proof of Theorem 5.16 in [QQ]