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Beyond the Kähler cone. (English) Zbl 0847.32034

Teicher, Mina (ed.), Proceedings of the Hirzebruch 65 conference on algebraic geometry, Bar-Ilan University, Ramat Gan, Israel, May 2-7, 1993. Ramat-Gan: Bar-Ilan University, Isr. Math. Conf. Proc. 9, 361-376 (1996).
From the author’s abstract: “The moduli space of nonlinear \(\sigma\)-models on a Calabi-Yau manifold contains a complexification of the Kähler cone of the manifold. The author describe a physically natural analytic continuation process which links the complexified Kähler cones of birationally equivalent Calabi-Yau manifolds. The enlarged moduli space includes a complexification of Kawamata’s “movable cone”. It is formulated a natural conjecture about the action of the birational automorphism group on this cone: There is a rational polyhedral cone \({\mathcal P} \subset H^2 (X, \mathbb{R})\), where \(X\) is a Calabi-Yau manifold, the union of whose translates \(\gamma ({\mathcal P})\) by birational automorphisms \(\gamma \in Bir ({\mathcal X}_t)\) covers the cone \(Mov ({\mathcal X}_t)_+\)”.
For the entire collection see [Zbl 0828.00035].

MSC:

32J81 Applications of compact analytic spaces to the sciences
32G81 Applications of deformations of analytic structures to the sciences
14J30 \(3\)-folds
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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