Results 21 to 30 of about 179 (53)

Semistable degenerations of Calabi–Yau manifolds and mirror P=W conjectures

Forum of Mathematics, Sigma
Mirror symmetry for a semistable degeneration of a Calabi–Yau manifold was first investigated by Doran–Harder–Thompson when the degenerate fiber is a union of two quasi-Fano manifolds.
Sukjoo Lee
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

Family Floer mirror space for local SYZ singularities

Forum of Mathematics, Sigma
We give a mathematically precise statement of the SYZ conjecture between mirror space pairs and prove it for any toric Calabi-Yau manifold with the Gross Lagrangian fibration. To date, it is the first time we realize the SYZ proposal with singular fibers
Hang Yuan
doaj   +1 more source

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

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 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  

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

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

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  

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