Beyond the Kähler cone

Abstract

The moduli space of nonlinear $\sigma$-models on a Calabi--Yau manifold contains a complexification of the Kähler cone of the manifold. We 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''. We formulate a natural conjecture about the action of the birational automorphism group on this cone. (Based in part on joint work with Paul Aspinwall and Brian Greene; submitted to the proceedings of ``Hirzebruch's 65th birthday workshop in algebraic geometry''.)

19 pages, AmS-TeX 2.1, DUK-M-94-04

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