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  "path": "/abs/2605.05621v1",
  "publishedAt": "2026-05-08T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Robert Andrews",
    "Abhibhav Garg"
  ],
  "textContent": "**Authors:** Robert Andrews, Abhibhav Garg\n\nWe study the question of explicitly constructing variety-evasive subspace families, a pseudorandom primitive introduced by Guo (Computational Complexity 2024) that generalizes both hitting sets and lossless rank condensers. Roughly speaking, a variety-evasive subspace family $\\mathcal{H}$ is a collection of subspaces such that for every algebraic variety $V$ in a fixed family $\\mathcal{F}$, there is some subspace $W \\in \\mathcal{H}$ that is in general position with respect to $V$. We give an explicit construction of a subspace families that evade all degree-$d$ varieties in an $n$-dimensional affine or projective space. Our construction improves on the size of the variety-evasive subspace families constructed by Guo and, for varieties of degree $n^{1 + Ω(1)}$, comes within a polynomial factor of Guo's lower bound on the size of any such variety-evasive subspace family. Our variety-evasive subspace families rely on an improved construction of hitting sets for Chow forms of algebraic varieties.",
  "title": "An Improved Construction of Variety-Evasive Subspace Families"
}