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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, released April 23, 2018, updated June 27, 2020.

Citation

If you have used this package in your research, please cite it as follows:

@misc{CorrespondenceScrollsSource,
  title = {{CorrespondenceScrolls: A \emph{Macaulay2} package. Version~0.6}},
  author = {David Eisenbud and Frank-Olaf Schreyer and Alessio Sammartano},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/stable/M2/Macaulay2/packages}}
}

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 a package, defined in CorrespondenceScrolls.m2.


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/CorrespondenceScrolls.m2:334:0.