Examples of Mori dream spaces with Picard number two (Q470878)

In the paper under review, the author gives a sufficient condition such that a projective variety with Picard number 2 is a Mori dream space. Using this result, the author shows that intersections of general hyperplanes of low degree in \(\mathbb P ^N\) (or in \(\mathbb P ^1\times \mathbb P ^N\)) are Mori dream spaces. Recall that a Mori dream space is a normal, projective, \(\mathbb Q\)-factorial variety such that \({\text{Pic}}(X)_{\mathbb Q} =N^1(X)_{\mathbb Q}\), \({\text{Nef}}(X)\) is the affine hull of finitely many semiample line bundles and there is a finite collection of small \(\mathbb Q\)-factorial modifications \(f_i:X\dasharrow X_i\) such that \({\text{Mov}}(X)=\bigcup_i f_i^*({\text{Nef}}(X_i))\) where for all \(i\), \({\text{Nef}}(X_i)\) is the affine hull of finitely many semiample line bundles.