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Дисертації з теми "Strict Calabi-Yau 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
Mishra, Challenger. "Calabi-Yau manifolds, discrete symmetries and string theory." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:4a174981-085e-4e81-8f27-b48533f08315.
Davies, Rhys. "Calabi-Yau threefolds and heterotic string compactification." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:be92aac5-6874-431e-95a0-ac61a88ee63d.
Cui, Wei. "Applications of Numerical Methods in Heterotic Calabi-Yau Compactification." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/99859.
Doctor of Philosophy
String theory is one of the most promising attempts to unify gravity with the other three fundamental interactions (electromagnetic, weak and strong) of nature. It is believed to give a self-consistent theory of quantum gravity, which, at low energy, could contain all of the physics that we known, from the Standard Model of particle physics to cosmology. String theories are often defined in nine spatial dimensions. To obtain a theory with three spatial dimensions one needs to hide, or ``compactify," six of the dimensions on a compact space which is small enough to have remained unobserved by our experiments. Unfortunately, the geometries of these spaces, called Calabi-Yau manifolds, and additional structures associated to them, called holomorphic vector bundles, turns out to be extremely complex. The equations determining the exact solutions of string theory for these quantities are highly non-linear partial differential equations (PDE's) which are simply impossible to solve analytically with currently known techniques. Nevertheless, knowledge of these solutions is critical in understanding much of the detailed physics that these theories imply. For example, to compute how the particles seen in three dimensions would interact with each other in a string theoretic model, the explicit form of these solutions would be required. Fortunately, numerical methods do exist for finding approximate solutions to the PDE's of interest. In this thesis we implement these algorithmic techniques and use them to study a variety of physical questions associated to the attempt to link string theory to the physics observed in our experiments.
Constantin, Andrei. "Heterotic string models on smooth Calabi-Yau threefolds." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:30be3aee-ba9b-4417-9b00-ee26a6bd67c5.
Andreas, Björn. "N=1 Heterotic / F-Theory Duality." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 1998. http://dx.doi.org/10.18452/14368.
We discuss aspects of N = 1 duality between the heterotic string compactified on a Calabi-Yau threefold with a vector bundle and F-theory on a Calabi-Yau fourfold. After a description of string duality intended for the non-specialist the framework and the constraints for heterotic/F-theory compactifications are presented. The computations of the necessary Calabi-Yau manifold and vector bundle data, involving characteristic classes and bundle moduli, are given in detail. The eight- and six- dimensional dualities are reviewed. The matching of the spectrum of chiral multiplets and of the number of heterotic five-branes respectively F-theory three-branes, needed for anomaly cancellation in four-dimensional vacua, is pointed out. Several examples of four-dimensional dual pairs are constructed where on both sides the geometry of the involved manifolds relies on del Pezzo surfaces.
Björk, Kevin. "Embedding inflation in string theory." Thesis, Uppsala universitet, Teoretisk fysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-392100.
Park, Hyukjae. "Aspects of string theory compactifications." Thesis, 2004. http://hdl.handle.net/2152/1284.
Park, Hyukjae Distler Jacques. "Aspects of string theory compactifications." 2004. http://wwwlib.umi.com/cr/utexas/fullcit?p3143440.
Книги з теми "Strict Calabi-Yau manifolds":
AMS-IMS-SIAM Joint Summer Research Conference on String Geometry (2004). Snowbird lectures on string geometry: Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on String Geometry, June 5-11, 2004, Snowbird, Utah. Edited by Becker Katrin 1967-. Providence, R.I: American Mathematical Society, 2006.
Kostov, Ivan. String theory. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.31.
Becker, Katrin, and AMS-IMS-SIAM JOINT SUMMER RESEARCH CONFE. Snowbird Lectures on String Geometry. American Mathematical Society, 2006.
Тези доповідей конференцій з теми "Strict Calabi-Yau manifolds":
Tian, Gang. "Smoothness of the Universal Deformation Space of Compact Calabi-Yau Manifolds and Its Peterson-Weil Metric." In Proceedings of the Conference on Mathematical Aspects of String Theory. WORLD SCIENTIFIC, 1987. http://dx.doi.org/10.1142/9789812798411_0029.