CorrespondenceScrolls -- Package to compute and analyze examples of Correspondence Scrolls

Description

Correspondence Scrolls generalize rational normal scrolls and K3 Carpets, among other familiar constructions. Suppose that Z is a subscheme of a product of projective spaces Z \subset P^{a_0} x .. x P^{a_{n-1}} The Correspondence Scroll C(Z;b), where b = (b_0,..,b_{n-1}) is the subscheme of P^{N-1} consisting set theoretically of the planes spanned by the points of the Segre-Veronese embedding corresponding to Z.

More generally, we treat the case of a multi-homogeneous subscheme Z' \subset A^{a_0-1} x .. x A^{a_{n-1}-1}.

Authors

Version

This documentation describes version 0.6 of CorrespondenceScrolls.

Source code

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

Exports

Functions and commands
- carpet -- ideal of a K3 carpet
- correspondencePolynomial -- computes the Hilbert polynomial of a correspondence scroll
- correspondenceScroll -- Union of planes joining points of rational normal curves according to a given correspondence
- hankelMatrix -- matrix with constant anti-diagonal entries
- irrelevantIdeal -- returns the irrelevant ideal of a multi-graded ring
- multiHilbertPolynomial -- Multi-graded Hilbert polynomial for a product of projective spaces
- productOfProjectiveSpaces -- Constructs the multi-graded ring of a product of copies of P^1 (pp is a synonym)
- schemeInProduct -- multi-graded Ideal of the image of a map to a product of projective spaces
- smallDiagonal -- Ideal of the small diagonal in (P^1)^n
Methods
- carpet(List) -- see carpet -- ideal of a K3 carpet
- correspondencePolynomial(Module,List) -- see correspondencePolynomial -- computes the Hilbert polynomial of a correspondence scroll
- correspondenceScroll(Ideal,List) -- see correspondenceScroll -- Union of planes joining points of rational normal curves according to a given correspondence
- hankelMatrix(Matrix,ZZ,ZZ) -- see hankelMatrix -- matrix with constant anti-diagonal entries
- hankelMatrix(Ring,RingElement,ZZ,ZZ) -- see hankelMatrix -- matrix with constant anti-diagonal entries
- hankelMatrix(Ring,ZZ,ZZ) -- see hankelMatrix -- matrix with constant anti-diagonal entries
- hankelMatrix(ZZ,ZZ) -- see hankelMatrix -- matrix with constant anti-diagonal entries
- hankelMatrix(ZZ,ZZ,String) -- see hankelMatrix -- matrix with constant anti-diagonal entries
- multiHilbertPolynomial(Module) -- see multiHilbertPolynomial -- Multi-graded Hilbert polynomial for a product of projective spaces
- productOfProjectiveSpaces(List) -- see productOfProjectiveSpaces -- Constructs the multi-graded ring of a product of copies of P^1 (pp is a synonym)
- productOfProjectiveSpaces(ZZ) -- see productOfProjectiveSpaces -- Constructs the multi-graded ring of a product of copies of P^1 (pp is a synonym)
- schemeInProduct(Ideal,List) -- see schemeInProduct -- multi-graded Ideal of the image of a map to a product of projective spaces
- schemeInProduct(Ideal,List,Ring) -- see schemeInProduct -- multi-graded Ideal of the image of a map to a product of projective spaces
- smallDiagonal(Ring) -- see smallDiagonal -- Ideal of the small diagonal in (P^1)^n
- smallDiagonal(ZZ) -- see smallDiagonal -- Ideal of the small diagonal in (P^1)^n
Symbols
- CoefficientField -- symbol used to define the ground field in many routines
- VariableName -- symbol used to define the variable name in many routines

For the programmer

The object CorrespondenceScrolls is a package.