Restricted Secant Varieties of Grassmannians
Dalton Bidleman, Luke Oeding

TL;DR
This paper investigates the dimensions of restricted secant varieties of Grassmannians, providing a formula under certain conjectural conditions, with computational examples and potential applications to coding theory.
Contribution
It introduces a dimension formula for restricted secant varieties of Grassmannians linked to a major conjecture, and explores computational methods and applications.
Findings
Derived a formula for the dimension of restricted secant varieties assuming the Baur-Draisma-deGraaf Conjecture.
Provided computational examples using Macaulay2.
Suggested applications to coding theory.
Abstract
Restricted secant varieties of Grassmannians are constructed from sums of points corresponding to -planes with the restriction that their intersection has a prescribed dimension. We study dimensions of restricted secant of Grassmannians and relate them to the analogous question for secants of Grassmannians via an incidence variety construction. We define a notion of expected dimension and give a formula for the dimension of all restricted secant varieties of Grassmannians that holds if the Baur-Draisma-deGraaf Conjecture on non-defectivity of Grassmannians is true. We also demonstrate example calculations in Macaulay2, and point out ways to make these calculations more efficient. We also show a potential application to coding theory.
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Taxonomy
TopicsPhytoestrogen effects and research · Coding theory and cryptography · Tensor decomposition and applications
