  For a generic hypersurface $\mathbb{X}^{n-1} \subset
\mathbb{P}^n(\mathbb{C})$ of degree \[ d \,\geqslant\, n^{2n} \] (1)
$\mathbb{P}^n \big\backslash \mathbb{X}^{n-1}$ is Kobayashi-hyperbolically
imbedded in $\mathbb{P}^n$;
  (2) $\mathbb{X}^{n-1}$ is Kobayashi($\Leftrightarrow$ Brody)-hyperbolic.
  (1) improves Brotbek-Deng 1804.01719: $d \geqslant (n+2)^{n+3}\, (n+1)^{n+3}
= n^{2n}\,n^6\, \big(e^3+{\rm O}(\frac{1}{n}) \big)$.
  (2) supersedes Demailly 1801.04765: $d \geqslant \frac{1}{3}\, \big( e^1(n-1)
\big)^{2n} = n^{2n}\, e^{2n}\, \big( \frac{1}{3\, e^2} + {\rm O} (\frac{1}{n})
\big)$.
  The method gives in fact $d \geqslant \frac{n^{2n}}{{\sf const}^n}$ for $n
\geqslant N({\sf const})$ with any ${\sf const} > 1$.
