Rational linear subspaces of hypersurfaces over finite fields
Fix positive integers $n,r,d$. We show that if $n,r,d$ satisfy a suitable inequality, then any smooth hypersurface $X\subset \mathbb{P}^n$ defined over a finite field of characteristic $p$ sufficiently large contains a rational $r$-plane. Under more restrictive hypotheses on $n,r,d$ we show the same...
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| creator | Fernández, María Inés de Frutos Garai, Sumita Isham, Kelly Murayama, Takumi Smith, Geoffrey |
| description | Fix positive integers $n,r,d$. We show that if $n,r,d$ satisfy a suitable
inequality, then any smooth hypersurface $X\subset \mathbb{P}^n$ defined over a
finite field of characteristic $p$ sufficiently large contains a rational
$r$-plane. Under more restrictive hypotheses on $n,r,d$ we show the same result
without the assumption that $X$ is smooth or that $p$ is sufficiently large. |
| doi_str_mv | 10.48550/arxiv.2111.10976 |
| format | Article |
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$r$-plane. Under more restrictive hypotheses on $n,r,d$ we show the same result
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inequality, then any smooth hypersurface $X\subset \mathbb{P}^n$ defined over a
finite field of characteristic $p$ sufficiently large contains a rational
$r$-plane. Under more restrictive hypotheses on $n,r,d$ we show the same result
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| subjects | Mathematics - Algebraic Geometry |
| title | Rational linear subspaces of hypersurfaces over finite fields |
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