Results 1 to 10 of about 12 (12)
On genus one mirror symmetry in higher dimensions and the BCOV conjectures
Forum of Mathematics, Pi, 2022 The mathematical physicists Bershadsky–Cecotti–Ooguri–Vafa (BCOV) proposed, in a seminal article from 1994, a conjecture extending genus zero mirror symmetry to higher genera.
Dennis Eriksson +2 more
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The most efficient indifferentiable hashing to elliptic curves of j-invariant 1728
Journal of Mathematical Cryptology, 2022 This article makes an important contribution to solving the long-standing problem of whether all elliptic curves can be equipped with a hash function (indifferentiable from a random oracle) whose running time amounts to one exponentiation in the basic ...
Koshelev Dmitrii
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Smoothing toroidal crossing spaces
Forum of Mathematics, Pi, 2021 We prove the existence of a smoothing for a toroidal crossing space under mild assumptions. By linking log structures with infinitesimal deformations, the result receives a very compact form for normal crossing spaces.
Simon Felten, Matej Filip, Helge Ruddat
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Conic bundles that are not birational to numerical Calabi--Yau pairs [PDF]
Épijournal de Géométrie Algébrique, 2017 Let $X$ be a general conic bundle over the projective plane with branch curve of degree at least 19. We prove that there is no normal projective variety $Y$ that is birational to $X$ and such that some multiple of its anticanonical divisor is effective ...
János Kollár
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Tropically constructed Lagrangians in mirror quintic threefolds
Forum of Mathematics, Sigma, 2020 We use tropical curves and toric degeneration techniques to construct closed embedded Lagrangian rational homology spheres in a lot of Calabi-Yau threefolds. The homology spheres are mirror dual to the holomorphic curves contributing to the Gromov-Witten
Cheuk Yu Mak, Helge Ruddat
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Analytic continuation of better-behaved GKZ systems and Fourier-Mukai transforms [PDF]
Épijournal de Géométrie AlgébriqueWe study the relationship between solutions to better-behaved GKZ hypergeometric systems near different large radius limit points, and their geometric counterparts given by the $K$-groups of the associated toric Deligne-Mumford stacks. We prove that the $
Zengrui Han
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A cone conjecture for log Calabi-Yau surfaces
Forum of Mathematics, SigmaWe consider log Calabi-Yau surfaces $(Y, D)$ with singular boundary. In each deformation type, there is a distinguished surface $(Y_e,D_e)$ such that the mixed Hodge structure on $H_2(Y \setminus D)$ is split.
Jennifer Li
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Deformations of Calabi–Yau varieties with k-liminal singularities
Forum of Mathematics, SigmaThe goal of this paper is to describe certain nonlinear topological obstructions for the existence of first-order smoothings of mildly singular Calabi–Yau varieties of dimension at least $4$ .
Robert Friedman, Radu Laza
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Smoothing, scattering and a conjecture of Fukaya
Forum of Mathematics, PiIn 2002, Fukaya [19] proposed a remarkable explanation of mirror symmetry detailing the Strominger–Yau–Zaslow (SYZ) conjecture [47] by introducing two correspondences: one between the theory of pseudo-holomorphic curves on a Calabi–Yau manifold ...
Kwokwai Chan +2 more
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Calabi–Yau attractor varieties and degeneration of Hodge structure
Open PhysicsWe present an application of asymptotic Hodge theory to the study of the attractor locus in flux compactifications. Our strategy is to investigate attractor points arising at the boundary of moduli spaces, where the limiting mixed Hodge structures encode
Rahmati Mohammad Reza
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