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Published in:
2011 | OriginalPaper | Chapter
A survey of Torelli and monodromy results for holomorphic-symplectic varieties
Author : Eyal Markman
Published in: Complex and Differential Geometry
Publisher: Springer Berlin Heidelberg
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We survey recent results about the Torelli question for holomorphicsymplectic varieties. Following are the main topics. A Hodge theoretic Torelli theorem. A study of the subgroup WExc, of the isometry group of the weight 2 Hodge structure, generated by reflection with respect to exceptional divisors. A description of the birational Kähler cone as a fundamental domain for the WExc action on the positive cone. A proof of a weak version of Morrison’s movable cone conjecture. A description of the moduli spaces of polarized holomorphic symplectic varieties as monodromy quotients of period domains of type IV.