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Showing 1 to 16 of 16 for “"Calabi-yau Manifolds"”.
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CALABI-YAU MANIFOLDS OF TYPE A AND THE CONE CONJECTURE FOR HYPERELLIPTIC VARIETIES
A Calabi-Yau n-fold Y is a compact, complex, Kähler n-fold with trivial canonical bundle and h^{i,0}(Y)=0 for 0<1 and Oguiso and Sakurai classified them in dimension 3. In this thesis we provide higher dimensional examples that ensure the existence of Calabi-Yau manifolds of type A in all odd …
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Elliptic fibrations among toric hypersurface Calabi-Yau manifolds and mirror symmetry of fibrations
… genus one fibrations among toric hypersurface Calabi-Yau three folds by (1) constructing explicitly elliptically fibered Calabi-Yau threefolds with large Hodge numbers using Weierstrass model techniques motivated by F-theory, and comparing the Tate-tuned Wierstrass model set with the set of …
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Asymptotically cylindrical Calabi–Yau and special Lagrangian geometry
We study asymptotically cylindrical Calabi–Yau manifolds and their asymptotically cylindrical special Lagrangian submanifolds. As a prototype problem, we also consider an extension of Hodge theory to general asymptotically cylindrical manifolds. For our study of asymptotically cylindrical …
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Classification of base geometries in F-theory
… we compactify F-theory on elliptically fibered Calabi-Yau manifolds of various dimensions, we produce a large number of minimal supergravity models in six or four spacetime dimensions. In this thesis, I will describe a current classification program of these elliptic Calabi-Yau manifolds. …
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Extending the Geometric Tools of Heterotic String Compactification and Dualities
… general vector bundles on elliptically fibered Calabi-Yau geometries. In particular, we consider the case in which the Calabi-Yau fibration is not in Weierstrass form but can rather contain fibral divisors or multiple sections (i.e., a higher rank Mordell-Weil group). In these cases, general …
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Applications of Numerical Methods in Heterotic Calabi-Yau Compactification
… to several different problems in heterotic Calabi-Yau compactification. We review algorithms for computing both the Ricci-flat metric on Calabi-Yau manifolds and Hermitian Yang-Mills connections on poly-stable holomorphic vector bundles over those spaces. We apply the numerical techniques …
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On special Kähler metrics and hypersurfaces
Minimal surfaces in 3-manifolds play an important role in 3-dimensional geometry. In higher dimensions, there are special geometric structures, including Ricci-flat Kähler structures on complex manifolds. They are called Calabi-Yau manifolds. Generalizations include Kähler-Ricci soliton structures. …
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Geometry of Ricci-flat Kähler manifolds and some counterexamples
… work, we study geometry of Ricci-flat Kähler manifolds, and also provide some counterexample constructions. We study asymptotic behavior of complete Ricci-flat metrics at infinity and consider a construction of approximate Ricci-flat metrics on quasiprojective manifolds with a divisor with …
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Flux compactifications of Type II string theories under non-perturbative dualities
… theories on toroidal orbifolds and generalised Calabi-Yau manifolds and their transformations under a set of non-perturbative dualities. The dualities are the Type IIA-IIB exchanging T duality, the self-symmetry of Type IIB S duality, the non-trivial combination of the two, U duality, and the …
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Geometry of SU(3) Manifolds
<p>I study differential geometry of 6-manifolds endowed with various $SU(3)$ structures from three perspectives. The first is special Lagrangian geometry; The second is pseudo-Hermitian-Yang-Mills connections or more generally, $\omega$-anti-self dual instantons; The third is pseudo-holomorphic …
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Calibrations and minimal Lagrangian submanifolds
… be concerned with the geometry of minimal submanifolds in certain Riemannian manifolds which possess some special geometric structure. Those Riemannian manifolds will fall into one of the following categories: 1) A Riemannian manifold M with a calibrating k-form n7. We will derive some …
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Applications of gauged linear sigma models
… that RG flow to a new family of non-compact Calabi-Yau threefolds, constructed as fiber products of genus g curves and noncompact Kahler threefolds. We only considered curves given as branched double covers of P^1. Our construction utilizes nonperturbative constructions of the genus g curves, …
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A Study on Heterotic Target Space Duality – Bundle Stability/Holomorphy, F-theory and LG Spectra
… we consider TSD theories on elliptically fibered Calabi-Yau manifolds. In this context, each half of the "dual" heterotic theories must in turn have an F-theory dual. Moreover, the apparent relationship between two heterotic compactifications seen in (0,2) heterotic target space dual pairs should, …
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Spectral and Superpotential Effects in Heterotic Compactifications
… bundle morphisms between vec- tor bundles over Calabi-Yau manifolds, we show that this contribution to the superpotential vanishes in many cases. However, by working with more complicated, and realistic geome- tries, we also present examples where the Chern-Simons contribution to the …
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A geometric construction of a Calabi quasimorphism on projective space
… show that this quasimorphism agrees with the Calabi invariant for isotopies that are supported in displaceable subsets of CPⁿ.
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Shifted symplectic structures and derived moduli spaces
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms