Results 1 to 10 of about 11 (11)

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, Gerard Freixas i Montplet, Christophe Mourougane   +2 more
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

Analytic continuation of better-behaved GKZ systems and Fourier-Mukai transforms [PDF]

Épijournal de Géométrie Algébrique
We 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
doaj   +1 more source

A cone conjecture for log Calabi-Yau surfaces

Forum of Mathematics, Sigma
We 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
doaj   +1 more source

Deformations of Calabi–Yau varieties with k-liminal singularities

Forum of Mathematics, Sigma
The 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
doaj   +1 more source

Minimal log discrepancies of hypersurface mirrors

Forum of Mathematics, Sigma
For certain quasismooth Calabi–Yau hypersurfaces in weighted projective space, the Berglund-Hübsch-Krawitz (BHK) mirror symmetry construction gives a concrete description of the mirror.
Louis Esser
doaj   +1 more source

Nef cones of fiber products and an application to the cone conjecture

Forum of Mathematics, Sigma
We prove a decomposition theorem for the nef cone of smooth fiber products over curves, subject to the necessary condition that their Néron–Severi space decomposes.
Cécile Gachet, Hsueh-Yung Lin, Long Wang   +2 more
doaj   +1 more source