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arXiv · 2211.01469

Restricted Secant Varieties of Grassmannians

Dalton Bidleman·Luke Oeding
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Abstract

Restricted secant varieties of Grassmannians are constructed from sums of points corresponding to $k$-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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Dalton Bidleman, Luke Oeding. 2022-11-02. Restricted Secant Varieties of Grassmannians. https://doi.org/10.1007/s13348-023-00399-4

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