Joins, Secant Varieties and Their Associated Grassmannians

Edoardo Ballico ()
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Edoardo Ballico: Department of Mathematics, University of Trento, 38123 Povo, TN, Italy

Mathematics, 2024, vol. 12, issue 9, 1-20

Abstract: We prove a strong theorem on the partial non-defectivity of secant varieties of embedded homogeneous varieties developing a general set-up for families of subvarieties of Grassmannians. We study this type of problem in the more general set-up of joins of embedded varieties. Joins are defined by taking a closure. We study the set obtained before making the closure (often called the open part of the join) and the set added after making the closure (called the boundary of the join). For a point q of the open part, we give conditions for the uniqueness of the set proving that q is in the open part.

Keywords: joins; secant variety; Grassmannian; defective secant variety; solution sets of joins; boundaries of joins (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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