The Gale transform and multi-graded determinantal schemes

Susan M. Cooper, Steven P. Diaz

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 languageEnglish (US)
Pages (from-to)3120-3127
Number of pages8
JournalJournal of Algebra
Issue number8
StatePublished - Apr 15 2008


  • Determinantal subschemes
  • Gale transform
  • Veronese and Segre embeddings

ASJC Scopus subject areas

  • Algebra and Number Theory


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