Results 21 to 30 of about 160 (40)

Weak Mirror Symmetry of Complex Symplectic Algebras

, 2010
A complex symplectic structure on a Lie algebra $\lie h$ is an integrable complex structure $J$ with a closed non-degenerate $(2,0)$-form. It is determined by $J$ and the real part $\Omega$ of the $(2,0)$-form.
Andrada, Andrada, Andrada, Barannikov, Ben-Bassat, Besse, Cleyton, Cleyton, Fino, G.P. Ovando, Hitchin, Kamada, Merkulov, Poon, R. Cleyton, Strominger, Y.S. Poon, Zhou   +17 more
core   +1 more source

A framework for tropical mirror symmetry [PDF]

, 2011
Applying tropical geometry a framework for mirror symmetry, including a mirror construction for Calabi-Yau varieties, was proposed by the author. We discuss the conceptual foundations of this construction based on a natural mirror map identifying ...
Boehm, Janko
core  

Smoothing, scattering and a conjecture of Fukaya

Forum of Mathematics, Pi
In 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, Naichung Conan Leung, Ziming Nikolas Ma   +2 more
doaj   +1 more source

Strange duality of weighted homogeneous polynomials

, 2010
We consider a mirror symmetry between invertible weighted homogeneous polynomials in three variables. We define Dolgachev and Gabrielov numbers for them and show that we get a duality between these polynomials generalizing Arnold's strange duality ...
Arnold, Atsushi Takahashi, Ebeling, Saito, Takahashi, Wolfgang Ebeling   +5 more
core   +1 more source

Mirror symmetry for Pfaffian Calabi-Yau 3-folds via conifold transitions [PDF]

, 2017
In this note we construct conifold transitions between several Calabi-Yau threefolds given by Pfaffians in weighted projective spaces and Calabi-Yau threefolds appearing as complete intersections in toric varieties. We use the obtained results to predict
Kapustka, Michal
core  

A Hypergeometric Version of the Modularity of Rigid Calabi-Yau Manifolds

, 2018
We examine instances of modularity of (rigid) Calabi-Yau manifolds whose periods are expressed in terms of hypergeometric functions. The $p$-th coefficients $a(p)$ of the corresponding modular form can be often read off, at least conjecturally, from the ...
Zudilin, Wadim
core   +2 more sources

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

Classifications of elliptic fibrations of a singular K3 surface

, 2015
We classify, up to automorphisms, the elliptic fibrations on the singular K3 surface $X$ whose transcendental lattice is isometric to $\langle 6\rangle\oplus \langle 2\rangle$.Comment: 28 ...
Bertin, Marie José, Garbagnati, Alice, Hortsch, Ruthi, Lecacheux, Odile, Mase, Makiko, Salgado, Cecília, Whitcher, Ursula   +6 more
core   +1 more source

Tropical mirror symmetry for elliptic curves

, 2017
Mirror symmetry relates Gromov-Witten invariants of an elliptic curve with certain integrals over Feynman graphs. We prove a tropical generalization of mirror symmetry for elliptic curves, i.e., a statement relating certain labeled Gromov-Witten ...
Boehm, Janko, Bringmann, Kathrin, Buchholz, Arne, Markwig, Hannah   +3 more
core   +1 more source

A Mirror Theorem for Toric Stacks

, 2014
We prove a Givental-style mirror theorem for toric Deligne--Mumford stacks X. This determines the genus-zero Gromov--Witten invariants of X in terms of an explicit hypergeometric function, called the I-function, that takes values in the Chen--Ruan ...
Coates, Tom, Corti, Alessio, Iritani, Hiroshi, Tseng, Hsian-Hua   +3 more
core   +1 more source