Results 1 to 10 of about 257,471 (64)
Hyperbolic geometry of the ample cone of a hyperkähler manifold [PDF]
Research in the Mathematical Sciences, 2015 Let M be a compact hyperkähler manifold with maximal holonomy (IHS). The group $$H^2(M, {\mathbb {R}})$$H2(M,R) is equipped with a quadratic form of signature $$(3, b_2-3)$$(3,b2-3), called Bogomolov–Beauville–Fujiki form.
E. Amerik, M. Verbitsky
semanticscholar +2 more sources
On the Alesker-Verbitsky Conjecture on HyperKähler Manifolds [PDF]
Geometric and Functional Analysis, 2021 We solve the quaternionic Monge–Ampère equation on hyperKähler manifolds. In this way we prove the ansatz for the conjecture raised by Alesker and Verbitsky claiming that this equation should be solvable on any hyperKähler with torsion manifold, at least
S. Dinew, Marcin Sroka
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Complex Lagrangians in a hyperKähler manifold and the relative Albanese [PDF]
, 2020 Let M be the moduli space of complex Lagrangian submanifolds of a hyperKähler manifold X, and let ω̄ : 𝒜̂ → M be the relative Albanese over M. We prove that 𝒜̂ has a natural holomorphic symplectic structure.
I. Biswas, T. G'omez, André G. Oliveira
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Hyperkähler geometry of rational curves in twistor spaces [PDF]
Complex Manifolds, 2021 We investigate the pseudo-hyperkähler geometry of higher degree rational curves in the twistor space of a hyperkähler 4-manifold.
R. Bielawski, Naizhen Zhang
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Sp(1)-symmetric hyperkähler quantisation [PDF]
Pacific Journal of Mathematics, 2021 We provide a new general scheme for the geometric quantisation of $\operatorname{Sp}(1)$-symmetric hyper-K\"ahler manifolds, considering Hilbert spaces of holomorphic sections with respect to the complex structures in the hyper-K\"ahler 2-sphere.
J. Andersen +2 more
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Locality in the Fukaya category of a hyperkähler manifold [PDF]
Compositio Mathematica, 2018 Let $(M,I,J,K,g)$ be a hyperkähler manifold. Then the complex manifold $(M,I)$ is holomorphic symplectic. We prove that for all real $x,y$ , with $x^{2}+y^{2}=1$ except countably many, any finite-energy $(xJ+yK)$ -holomorphic curve with boundary in a ...
Jake Solomon, M. Verbitsky
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THE SPACE OF HYPERKÄHLER METRICS ON A 4-MANIFOLD WITH BOUNDARY [PDF]
Forum of Mathematics, Sigma, 2016 Let $X$ be a compact 4-manifold with boundary. We study the space of hyperkähler triples $\unicode[STIX]{x1D714}_{1},\unicode[STIX]{x1D714}_{2},\unicode[STIX]{x1D714}_{3}$ on $X$ , modulo diffeomorphisms which are the identity on the boundary.
J. Fine, Jason D. Lotay, M. Singer
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Complex hyperkähler structures defined by Donaldson–Thomas invariants [PDF]
Letters in Mathematical Physics, 2020 The notion of a Joyce structure was introduced in Bridgeland (Geometry from Donaldson–Thomas invariants, preprint arXiv:1912.06504) to describe the geometric structure on the space of stability conditions of a CY3\documentclass[12pt]{minimal} \usepackage{
T. Bridgeland, I. Strachan
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Monodromy of subrepresentations and irreducibility of low degree automorphic Galois representations
Journal of the London Mathematical Society, Volume 108, Issue 6, Page 2436-2490, December 2023., 2023 Abstract Let X$X$ be a smooth, separated, geometrically connected scheme defined over a number field K$K$ and {ρλ:π1(X)→GLn(Eλ)}λ$\lbrace \rho _\lambda :\pi _1(X)\rightarrow \mathrm{GL}_n(E_\lambda )\rbrace _\lambda$ a system of semisimple λ$\lambda$‐adic representations of the étale fundamental group of X$X$ such that for each closed point x$x$ of X$X$
Chun Yin Hui
wiley +1 more source
Positivity of Riemann–Roch polynomials and Todd classes of hyperkähler manifolds [PDF]
Journal of Algebraic Geometry, 2020 For a hyperkähler manifold X X of dimension 2 n 2n , Huybrechts showed that there are constants a 0 a_0 , a 2 a_2 , …,
Chen Jiang
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