294 research outputs found

    Geometric transitions and SYZ mirror symmetry

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    We prove that the punctured generalized conifolds and punctured orbifolded conifolds are mirror symmetric under the SYZ program with quantum corrections. This mathematically confirms the gauge-theoretic prediction by Aganagic-Karch-L\"ust-Miemiec, and also provides a supportive evidence to Morrison's conjecture that geometric transitions are reversed under mirror symmetry.Comment: v3: one compact example added. 25 pages, 12 figure

    Local Calabi-Yau manifolds of type \tilde{A} via SYZ mirror symmetry

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    We carry out the SYZ program for the local Calabi--Yau manifolds of type A~\widetilde{A} by developing an equivariant SYZ theory for the toric Calabi--Yau manifolds of infinite-type. Mirror geometry is shown to be expressed in terms of the Riemann theta functions and generating functions of open Gromov--Witten invariants, whose modular properties are found and studied in this article. Our work also provides a mathematical justification for a mirror symmetry assertion of the physicists Hollowood--Iqbal--Vafa.Comment: v3: 43 pages, 12 figures, improved expositio

    Mirror symmetry and rigid structures of generalized K3 surfaces

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    The present article is concerned with mirror symmetry for generalized K3 surfaces, with particular emphasis on complex and K\"ahler rigid structures. Inspired by the works of Dolgachev, Aspinwall-Morrison and Huybrechts, we introduce a formulation of mirror symmetry for generalized K3 surfaces. As an application, we settle the long-standing problem of mirror symmetry for singular K3 surfaces. Along the way, we investigate complex and K\"ahler rigid structures of generalized K3 surfaces.Comment: restore some definitions, add some explanation

    Analysis of the phenomenon of speculative trading in one of its basic manifestations: postage stamp bubbles

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    We document and analyze the empirical facts concerning one of the clearest evidence of speculation in financial trading as observed in the postage collection stamp market. We unravel some of the mechanisms of speculative behavior which emphasize the role of fancy and collective behavior. In our conclusion, we propose a classification of speculative markets based on two parameters, namely the amplitude of the price peak and a second parameter that measures its ``sharpness''. This study is offered to anchor modeling efforts to realistic market constraints and observations.Comment: 9 pages, 5 figures and 2 tables, in press in Int. J. Mod. Phys.

    What Orchestrates the Self-Assembly of Glycine Molecules on Cu(100)?

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    The structures of two competing phases and their interrelationship in the self-organization of glycine molecules on a Cu(100) surface were clarified. Despite their similar structural energies predicted using first-principles calculation, completely different mechanisms were found to stabilize the two phases. The balance and coordination of the two mechanisms that induce a variety of self-assembled structures in this attractive system were revealed. Furthermore, the importance of the microscopic arrangement of the molecules in designing the macroscopic electronic structures was directly demonstrated
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