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Nef cone of a generalized Kummer 4-fold. (English) Zbl 1473.14077

K. Yoshioka [Adv. Stud. Pure Math. 69, 473–537 (2016; Zbl 1375.14066)] gave a lattice-theoretic description of the movable and nef cones of the generalized Kummer manifolds \(\operatorname{Km}^{(l-1)}(A)\) for \(l \ge 3\) of an abelian surface \(A\) of Picard rank \(1\). The paper under review gives a refined description in the case \(l=3\), i.e., in the case of the Kummer 4-fold. It claims that the boundary of the movable and nef cones are characterized by the Pell equation of particular form (Theorem 0.1).

MSC:

14J35 \(4\)-folds

Citations:

Zbl 1375.14066
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References:

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