Mori, Akira Nef cone of a generalized Kummer 4-fold. (English) Zbl 1473.14077 Hokkaido Math. J. 50, No. 2, 151-163 (2021). 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). Reviewer: Shintaro Yanagida (Nagoya) Cited in 1 Document MSC: 14J35 \(4\)-folds Keywords:generalized Kummer 4-fold; movable cone; nef cone Citations:Zbl 1375.14066 PDFBibTeX XMLCite \textit{A. Mori}, Hokkaido Math. J. 50, No. 2, 151--163 (2021; Zbl 1473.14077) Full Text: DOI arXiv References: [1] Beauville A., Variétés Kähleriennes dont la première classe de Chern est nulle. J. Diff. Geom. 18 (1983), 755-782. · Zbl 0537.53056 [2] Namikawa Y., Counter-example to global Torelli problem for irreducible symplectic manifolds. Math. Ann. 324 (2002), 841-845. · Zbl 1028.53081 [3] Wierzba J. and Wiśniewski J. A., Small contractions of symplectic 4-folds. Duke Math. J. 120 (2003), 65-95. · Zbl 1036.14007 [4] Yanagida S. and Yoshioka K., Semi-homogeneous sheaves, Fourier-Mukai transforms and moduli of stable sheaves on Abelian surfaces. J. reine angew. Math. 684 (2013), 31-86. · Zbl 1401.14100 [5] Yoshioka K., Moduli spaces of stable sheaves on abelian surfaces. Math. Ann. 321 (2001), 817-884. · Zbl 1066.14013 [6] Yoshioka K., Bridgeland’s stability and the positive cone of the moduli spaces of stable objects on an abelian surface. Adv. Stub. Pure Math. 69 (2016), 473-537. · Zbl 1375.14066 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.