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Статті в журналах з теми "Hyper-Kähler manifolds":
Dancer, A. "Hyper-Kähler manifolds." Surveys in Differential Geometry 6, no. 1 (2001): 15–38. http://dx.doi.org/10.4310/sdg.2001.v6.n1.a2.
Beckmann, Thorsten. "Derived categories of hyper-Kähler manifolds: extended Mukai vector and integral structure." Compositio Mathematica 159, no. 1 (January 2023): 109–52. http://dx.doi.org/10.1112/s0010437x22007849.
Merker, Jochen. "On Almost Hyper-Para-Kähler Manifolds." ISRN Geometry 2012 (March 8, 2012): 1–13. http://dx.doi.org/10.5402/2012/535101.
Entov, Michael, and Misha Verbitsky. "Unobstructed symplectic packing for tori and hyper-Kähler manifolds." Journal of Topology and Analysis 08, no. 04 (September 8, 2016): 589–626. http://dx.doi.org/10.1142/s1793525316500229.
Alekseevsky, D. V., V. Cortés, and T. Mohaupt. "Conification of Kähler and Hyper-Kähler Manifolds." Communications in Mathematical Physics 324, no. 2 (October 6, 2013): 637–55. http://dx.doi.org/10.1007/s00220-013-1812-0.
GOTO, RYUSHI. "On toric hyper-Kähler manifolds given by the hyper-Kähler quotient method." International Journal of Modern Physics A 07, supp01a (April 1992): 317–38. http://dx.doi.org/10.1142/s0217751x92003835.
Krivonos, S. O., and A. V. Shcherbakov. "Hyper-Kähler manifolds and nonlinear supermultiplets." Physics of Particles and Nuclei Letters 4, no. 1 (February 2007): 55–59. http://dx.doi.org/10.1134/s1547477107010104.
Goto, R. "On hyper-Kähler manifolds of typeA ∞." Geometric and Functional Analysis 4, no. 4 (July 1994): 424–54. http://dx.doi.org/10.1007/bf01896403.
CAPPELLETTI MONTANO, BENIAMINO, ANTONIO DE NICOLA, and GIULIA DILEO. "THE GEOMETRY OF 3-QUASI-SASAKIAN MANIFOLDS." International Journal of Mathematics 20, no. 09 (September 2009): 1081–105. http://dx.doi.org/10.1142/s0129167x09005662.
BERGSHOEFF, ERIC, STEFAN VANDOREN, and ANTOINE VAN PROEYEN. "THE IDENTIFICATION OF CONFORMAL HYPERCOMPLEX AND QUATERNIONIC MANIFOLDS." International Journal of Geometric Methods in Modern Physics 03, no. 05n06 (September 2006): 913–32. http://dx.doi.org/10.1142/s0219887806001521.
Дисертації з теми "Hyper-Kähler manifolds":
Bai, Chenyu. "Hodge Theory, Algebraic Cycles of Hyper-Kähler Manifolds." Electronic Thesis or Diss., Sorbonne université, 2024. http://www.theses.fr/2024SORUS081.
This thesis is devoted to the study of algebraic cycles in projective hyper-Kähler manifolds and strict Calabi-Yau manifolds. It contributes to the understanding of Beauville's and Voisin's conjectures on the Chow rings of projective hyper-Kähler manifolds and strict Calabi-Yau manifolds. It also studies some birational invariants of projective hyper-Kähler manifolds.The first part of the thesis, appeared in Mathematische Zeitschrift [C. Bai, On Abel-Jacobi maps of Lagrangian families, Math. Z. 304, 34 (2023)] and presented in Chapter 2, studies whether the Lagrangian subvarieties in a hyper-Kähler manifold sharing the same cohomological class have the same Chow class as well. We study the notion of Lagrangian families and its associated Abel-Jacobi maps. We take an infinitesimal approach to give a criterion for the triviality of the Abel-Jacobi map of a Lagrangian family, and use this criterion to give a negative answer to the above question, adding to the subtleties of a conjecture of Voisin. We also explore how the maximality of the variation of the Hodge structures on the degree 1 cohomology the Lagrangian family implies the triviality of the Abel-Jacobi map. The second part of the thesis, to appear in International Mathematics Research Notices [C. Bai, On some birational invariants of hyper-Kähler manifolds, ArXiv: 2210.12455, to appear in International Mathematics Research Notices, 2024] and presented in Chapter 3, studies the degree of irrationality, the fibering gonality and the fibering genus of projective hyper-Kähler manifolds, with emphasis on the K3 surfaces case, en mettant l'accent sur le cas des surfaces K3. We first give a slight improvement of a result of Voisin on the lower bound of the degree of irrationality of Mumford-Tate general hyper-Kähler manifolds. We then study the relation of the above three birational invariants for projective K3 surfaces of Picard number 1, adding the understandinf of a conjecture of Bastianelli, De Poi, Ein, Lazarsfeld, Ullery on the asymptotic behavior of the degree of irrationality of very general projective K3 surfaces. The third part of the thesis, presented in Chapter 4, studies the higher dimensional Voisin maps on strict Calabi-Yau manifolds. Voisin constructed self-rational maps of Calabi-Yau manifolds obtained as varieties of r-planes in cubic hypersurfaces of adequate dimension. This map has been thoroughly studied in the case r=1, which is the Beauville-Donagi case. For higher dimensional cases, we first study the action of the Voisin map on the holomorphic forms. We then prove the generalized Bloch conjecture for the action of the Voisin maps on Chow groups for the case of r=2. Finally, via the study of the Voisin map, we provide evidence for a conjecture of Voisin on the existence of a special 0-cycle on strict Calabi-Yau manifolds
Haydys, Andriy. "Generalized Seiberg-Witten equations and hyperKähler geometry." Doctoral thesis, 2006. http://hdl.handle.net/11858/00-1735-0000-0006-B381-C.
Книги з теми "Hyper-Kähler manifolds":
Shen, Mingmin. The Fourier transform for certain hyper Kähler fourfolds. Providence, Rhode Island: American Mathematical Society, 2016.
Nieper-Wigbkirchen, Marc. Chern numbers and Rozansky-Witten invariants of compact hyper-Kähler manifolds. Singapore: World Scientific, 2005.
Gross, Mark, Dominic Joyce, and Daniel Huybrechts. Calabi-Yau Manifolds and Related Geometries. Springer, 2003.
Olson, Loren, Mark Gross, Dominic Joyce, Geir Ellingsrud, and Daniel Huybrechts. Calabi-Yau Manifolds and Related Geometries: Lectures at a Summer School in Nordfjordeid, Norway, June 2001. Springer London, Limited, 2012.
Voisin, Claire. Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187). Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691160504.001.0001.
Частини книг з теми "Hyper-Kähler manifolds":
LeBrun, Claude. "Twistors, Hyper-Kähler Manifolds, and Complex Moduli." In Springer INdAM Series, 207–14. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67519-0_8.
Hattori, Kota. "The Geometry on Hyper-Kähler Manifolds of Type A ∞." In Springer Proceedings in Mathematics & Statistics, 309–17. Tokyo: Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-55215-4_27.
Fré, Pietro Giuseppe. "(Hyper)Kähler Quotients, ALE-Manifolds and $$\mathbb {C}^n/\varGamma $$ Singularities." In Advances in Geometry and Lie Algebras from Supergravity, 447–551. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74491-9_8.
Voisin, Claire. "Torsion Points of Sections of Lagrangian Torus Fibrations and the Chow Ring of Hyper-Kähler Manifolds." In Geometry of Moduli, 295–326. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94881-2_10.
"Hyper-Kähler and HKT Manifolds." In Differential Geometry through Supersymmetric Glasses, 51–76. WORLD SCIENTIFIC, 2020. http://dx.doi.org/10.1142/9789811206788_0004.
"Mirror symmetry for hyper-Kähler manifolds." In Mirror Symmetry III, 115–56. Providence, Rhode Island: American Mathematical Society, 1998. http://dx.doi.org/10.1090/amsip/010/04.
"Compact hyper-Kähler manifolds and holomorphic symplectic manifolds." In Chern Numbers and Rozansky–Witten Invariants of Compact Hyper-Kähler Manifolds, 1–38. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812562357_0001.
"Graph homology." In Chern Numbers and Rozansky–Witten Invariants of Compact Hyper-Kähler Manifolds, 39–82. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812562357_0002.
"Rozansky–Witten theory." In Chern Numbers and Rozansky–Witten Invariants of Compact Hyper-Kähler Manifolds, 83–107. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812562357_0003.
"Calculations for the example series." In Chern Numbers and Rozansky–Witten Invariants of Compact Hyper-Kähler Manifolds, 109–39. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812562357_0004.