<p>We present constructions of small 2<i>n</i>-covers of the hyperbolic quadric <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(Q^+ (4n+1,q)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>Q</mi> <mo>+</mo> </msup> <mrow> <mo stretchy="false">(</mo> <mn>4</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. We also present a lower bound on the size of a 2<i>n</i>-cover of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(Q^+ (4n+1,q)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>Q</mi> <mo>+</mo> </msup> <mrow> <mo stretchy="false">(</mo> <mn>4</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>q</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Minimal 2n-covers of the hyperbolic quadric \(Q^+(4n+1,q)\)

  • Laure Schelfhout,
  • Leo Storme

摘要

We present constructions of small 2n-covers of the hyperbolic quadric \(Q^+ (4n+1,q)\) Q + ( 4 n + 1 , q ) . We also present a lower bound on the size of a 2n-cover of \(Q^+ (4n+1,q)\) Q + ( 4 n + 1 , q ) .