HyperKähler potentials in cohomogeneity two
نویسندگان
چکیده
منابع مشابه
Manifolds of Cohomogeneity Two
First, a word from our sponsor (particle physics). The mathematical reader should not expect to understand the physics, but (paraphrasing A. N. Varchenko) just let the words wash over you like music. Acharya & Witten [1] and Atiyah & Witten [2] have demonstrated that singularities in G2 holonomy manifolds 1 can compactify M -theory yielding effective quantum field theories in 3+1 dimensional Mi...
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 کاملHyperkähler Analogues of Kähler Quotients
Hyperkähler Analogues of Kähler Quotients by Nicholas James Proudfoot Doctor of Philosophy in Mathematics University of California, Berkeley Professor Allen Knutson, Chair Let X be a Kähler manifold that is presented as a Kähler quotient of Cn by the linear action of a compact group G. We define the hyperkähler analogue M of X as a hyperkähler quotient of the cotangent bundle T ∗Cn by the induc...
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: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2001
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crll.2001.011