A survey of Torelli and monodromy results for holomorphic-symplectic varieties

Details A survey of Torelli and monodromy results for holomorphic-symplectic varieties A survey of Torelli and monodromy results for holomorphic-symplectic varieties

2011-01-24

arxiv.org/abs/1101.4606v3

Proceedings of the conference "Complex and Differential Geometry'', Springer Proceedings in Mathematics, 2011, Volume 8, 257--

Mathematics

Algebraic Geometry

46 pages. v3: The previous attempt to simplify the statement of Conjecture 10.6 resulted in a false statement. The statement o

Scientific paper

10.1007/978-3-642-20300-8_15

We survey recent results about the Torelli question for holomorphic-symplectic varieties. Following are the main topics. A Hodge theoretic Torelli theorem. A study of the subgroup W, of the isometry group of the weight 2 Hodge structure, generated by reflection with respect to exceptional divisors. A description of the birational Kahler cone as a fundamental domain for the W-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.

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