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2 results

  • A NOTE ON RICH LINES IN TRULY HIGH DIMENSIONAL SETS

  • Part of
  • JOSHUA ZAHL
  • Journal:
    Forum of Mathematics, Sigma / Volume 4 / 2016
    Published online by Cambridge University Press:
    13 January 2016, e2
    • Article
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  • We modify an argument of Hablicsek and Scherr to show that if a collection of points in $\mathbb{C}^{d}$ spans many $r$ -rich lines, then many of these lines must lie in a common $(d-1)$ -flat. This is closely related to a previous result of Dvir and Gopi.

  • ON THE FREENESS OF 3-ARRANGEMENTS

  • MASAHIKO YOSHINAGA
  • Journal:
    Bulletin of the London Mathematical Society / Volume 37 / Issue 1 / January 2005
    Published online by Cambridge University Press:
    08 February 2005, pp. 126-134
    Print publication:
    January 2005

  • Hyperplane arrangements in a three-dimensional vector space are considered in this paper. A characterization of the freeness of such an arrangement is given in terms of the characteristic polynomial and a restricted multiarrangement. As an application, the freeness of cones over certain two-dimensional affine arrangements is proved.