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

## Description

Correspondence Scrolls generalize rational normal scrolls and K3 Carpets, among other familiar constuctions. 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-homogneous subscheme Z' \subset A^{a_0-1} x .. x A^{a_{n-1}-1}.

## 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
• 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 .