Compact hyperkähler manifolds: basic results
نویسندگان
چکیده
منابع مشابه
Period Maps and Cohomology Cohomology of Compact Hyperkähler Manifolds
Let M be a compact simply connected hy-perkähler (or holomorphically symplectic) manifold, dim H 2 (M) = n. Assume that M is not a product of hyperkaehler manifolds. We prove that the Lie group so(n−3, 3) acts by automorphisms on the cohomology ring H * (M). Under this action, the space H 2 (M) is isomorphic to the fundamental representation of so(n − 3, 3). Let A r be the subring of H * (M) ge...
متن کاملCohomology of Compact Hyperkähler Manifolds and Its Applications
This article contains a compression of results from [V], with most proofs omitted. We prove that every two points of the connected moduli space of holomorphically symplectic manifolds can be connected with so-called “twistor lines” – projective lines holomorphically embedded to the moduli space and corresponding to the hyperkähler structures. This has interesting implications for the geometry o...
متن کاملAlgebraic Structures on Hyperkähler Manifolds Algebraic Structures on Hyperkähler Manifolds
Let M be a compact hyperkähler manifold. The hy-perkähler structure equips M with a set R of complex structures parametrized by CP 1 , called the set of induced complex structures. It was known previously that induced complex structures are non-algebraic, except may be a countable set. We prove that a countable set of induced complex structures is algebraic, and this set is dense in R. A more g...
متن کاملMirror Symmetry for hyperkähler manifolds
We prove the Mirror Conjecture for Calabi-Yau manifolds equipped with a holomorphic symplectic form, also known as complex manifolds of hyperkähler type. We obtain that a complex manifold of hyperkähler type is mirror dual to itself. The Mirror Conjecture is stated (following Kontsevich, ICM talk) as the equivalence of certain algebraic structures related to variations of Hodge structures. We c...
متن کاملKobayashi pseudometric on hyperkähler manifolds
The Kobayashi pseudometric on a complex manifold M is the maximal pseudometric such that any holomorphic map from the Poincaré disk to M is distance-decreasing. Kobayashi has conjectured that this pseudometric vanishes on Calabi-Yau manifolds. Using ergodicity of complex structures, we prove this result for any hyperkähler manifold if it admits a deformation with a Lagrangian fibration, and its...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Inventiones Mathematicae
سال: 1999
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s002220050280