Results 21 to 30 of about 163 (41)

The KSBA moduli space of stable log Calabi–Yau surfaces

Forum of Mathematics, Pi
We prove that every irreducible component of the coarse Kollár-Shepherd-Barron and Alexeev (KSBA) moduli space of stable log Calabi–Yau surfaces admits a finite cover by a projective toric variety. This verifies a conjecture of Hacking–Keel–Yu. The proof
Valery Alexeev, Hulya Arguz, Pierrick Bousseau   +2 more
doaj   +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

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

Root, flow and order polytopes with connections to toric geometry

Forum of Mathematics, Sigma
In this paper, we study the class of polytopes which can be obtained by taking the convex hull of some subset of the points $\{e_i-e_j \ \vert \ i \neq j\} \cup \{\pm e_i\}$ in $\mathbb {R}^n$ , where $e_1,\dots ,e_n$ is the standard ...
Konstanze Rietsch, Lauren Kiyomi Williams   +1 more
doaj   +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  

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

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

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

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