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Showing 1 to 6 of 6 for “"Calabi-Yau threefold"”.
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Fibered Calabi -Yau Varieties and Toric Varieties
… constructing K3-fibered and elliptically fibered Calabi-Yau threefolds over P1 and P2 respectively. We first show how to write weighted projective space bundles as toric varieties. We then find necessary and sufficient conditions for the anti-canonical linear systems of these bundles to have …
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On the Modularity of Higher-Dimensional Varieties
… introduce Wiles' method to establish that a Calabi-Yau threefold defined over the field Q with 2-dimensional ℓ-adic cohomology is modular, answering a question of Saito & Yui. Second, we show that a quintic threefold with 4-dimensional middle cohomology is Hilbert modular. This answers a …
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Gopakumar-Vafa invariant and Macdonald formula
… that counts the number of curves inside a given Calabi-Yau threefold. The definition has been conjectured by Maulik-Toda in 2016 in terms of perverse sheaf. I will use this definition on the total space of canonical bundle of P2 and compute the associated invariants. I will introduce a …
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Towards studying of the higher rank theory of stable pairs
… Pandharipande-Thomas theory of stable pairs on a Calabi-Yau threefold $X$. More precisely, we develop a moduli theory for frozen triples given by the data $\mathcal{O}_X^{\oplus r}(-n)\xrightarrow{\phi} F$ where $F$ is a sheaf of pure dimension $1$. The moduli space of such objects does not …
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Calibrations and minimal Lagrangian submanifolds
… (n, 0)-form (we will call'M an almost Calabi-Yau manifold). We will study the geometry of Special Lagrangian submanifolds on M and the global properties of their moduli-space. We will exhibit an example of a compact, simply connected almost Calabi-Yau threefold, which admits a Special …
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Branes, graphs and singularities
… for D-branes probing singular non-compact Calabi-Yau spaces with toric symmetries. Brane tilings also offer a generalization of the AdS/CFT correspondence. A technique is developed which enables one to quickly compute the toric vacuum moduli space of the quiver gauge theory. The equivalence …