The Gale transform and multi-graded determinantal schemes

Susan M. Cooper; Steven P. Diaz

doi:10.1016/j.jalgebra.2007.11.013

The Gale transform and multi-graded determinantal schemes

Susan M. Cooper, Steven P. Diaz

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Eisenbud and Popescu showed that certain finite determinantal subschemes of projective spaces defined by maximal minors of adjoint matrices of homogeneous linear forms are related by Veronese embeddings and a Gale transform. We extend this result to adjoint matrices of multihomogeneous multilinear forms. The subschemes now lie in products of projective spaces and the Veronese embeddings are replaced with Segre embeddings.

Original language	English (US)
Pages (from-to)	3120-3127
Number of pages	8
Journal	Journal of Algebra
Volume	319
Issue number	8
DOIs	https://doi.org/10.1016/j.jalgebra.2007.11.013
State	Published - Apr 15 2008

Keywords

Determinantal subschemes
Gale transform
Veronese and Segre embeddings

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2007.11.013

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AU - Diaz, Steven P.

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AB - Eisenbud and Popescu showed that certain finite determinantal subschemes of projective spaces defined by maximal minors of adjoint matrices of homogeneous linear forms are related by Veronese embeddings and a Gale transform. We extend this result to adjoint matrices of multihomogeneous multilinear forms. The subschemes now lie in products of projective spaces and the Veronese embeddings are replaced with Segre embeddings.

KW - Determinantal subschemes

KW - Gale transform

KW - Veronese and Segre embeddings

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The Gale transform and multi-graded determinantal schemes

Abstract

Keywords

ASJC Scopus subject areas

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