scholarly journals J FUNCTIONS, NON-NEF TORIC VARIETIES AND EQUIVARIANT LOCAL MIRROR SYMMETRY OF CURVES

2007 ◽  
Vol 22 (13) ◽  
pp. 2327-2360 ◽  
Author(s):  
BRIAN FORBES ◽  
MASAO JINZENJI
Keyword(s):  
Mirror Symmetry ◽  
Toric Varieties ◽  
Computational Scheme ◽  
Birkhoff Factorization ◽  
Local Mirror Symmetry

We provide a straightforward computational scheme for the equivariant local mirror symmetry of curves, i.e. mirror symmetry for [Formula: see text] for k ≥ 1, and detail related methods for dealing with mirror symmetry of non-nef toric varieties, based on the theorems of Refs. 2 and 13. The basic tools are equivariant I functions and their Birkhoff factorization.

scholarly journals [N′-(4-Decyloxy-2-oxidobenzylidene)-3-hydroxy-2-naphthohydrazidato-κ3N,O,O′]dimethyltin(IV): crystal structure and Hirshfeld surface analysis

2017 ◽  
Vol 73 (3) ◽  
pp. 390-396
Author(s):  
Siti Nadiah Binti Mohd Rosely ◽  
Rusnah Syahila Duali Hussen ◽  
See Mun Lee ◽  
Nathan R. Halcovitch ◽  
Mukesh M. Jotani ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Mirror Symmetry ◽  
Chelate Ring ◽  
Hirshfeld Surface ◽  
Methyl Groups ◽  
Coordination Geometry ◽  
Trigonal Bipyramidal ◽  
First Approximation ◽  
Benzene Rings ◽  
Local Mirror Symmetry

The title diorganotin compound, [Sn(CH3)2(C28H32N2O4)], features a distorted SnC2NO2coordination geometry almost intermediate between ideal trigonal–bipyramidal and square-pyramidal. The dianionic Schiff base ligand coordinates in a tridentate fashionviatwo alkoxide O and hydrazinyl N atoms; an intramolecular hydroxy-O—H...N(hydrazinyl) hydrogen bond is noted. The alkoxy chain has an all-transconformation, and to the first approximation, the molecule has local mirror symmetry relating the two Sn-bound methyl groups. Supramolecular layers sustained by imine-C—H...O(hydroxy), π–π [between decyloxy-substituted benzene rings with an inter-centroid separation of 3.7724 (13) Å], C—H...π(arene) and C—H...π(chelate ring) interactions are formed in the crystal; layers stack along thecaxis with no directional interactions between them. The presence of C—H...π(chelate ring) interactions in the crystal is clearly evident from an analysis of the calculated Hirshfeld surface.

scholarly journals Quantum Cohomology and Closed-String Mirror Symmetry for Toric Varieties

2020 ◽  
Vol 71 (2) ◽  
pp. 395-438
Author(s):  
Jack Smith
Keyword(s):  
Toric Variety ◽  
Mirror Symmetry ◽  
Complex Structure ◽  
Toric Varieties ◽  
Quantum Cohomology ◽  
Closed String ◽  
Generalized Jacobian ◽  
Novikov Ring

Abstract We give a short new computation of the quantum cohomology of an arbitrary smooth (semiprojective) toric variety $X$, by showing directly that the Kodaira–Spencer map of Fukaya–Oh–Ohta–Ono defines an isomorphism onto a suitable Jacobian ring. In contrast to previous results of this kind, $X$ need not be compact. The proof is based on the purely algebraic fact that a class of generalized Jacobian rings associated to $X$ are free as modules over the Novikov ring. When $X$ is monotone the presentation we obtain is completely explicit, using only well-known computations with the standard complex structure.

scholarly journals Summing the instantons: Quantum cohomology and mirror symmetry in toric varieties

1995 ◽  
Vol 440 (1-2) ◽  
pp. 279-354 ◽  
Author(s):  
David R. Morrison ◽  
M.Ronen Plesser
Keyword(s):  
Mirror Symmetry ◽  
Toric Varieties ◽  
Quantum Cohomology

scholarly journals Goodness of Regularity in Dot Patterns: Global Symmetry, Local Symmetry, and Their Interactions

Perception ◽  
10.1068/p5794 ◽  
2007 ◽  
Vol 36 (9) ◽  
pp. 1305-1319 ◽  
Author(s):  
Massimo Nucci ◽  
Johan Wagemans
Keyword(s):  
Mirror Symmetry ◽  
Local Symmetry ◽  
Detection Task ◽  
Global Symmetry ◽  
Different Types ◽  
Operational Models ◽  
Local Mirror Symmetry ◽  
Axes Of Symmetry ◽  
Global And Local ◽  
Short Presentation

Goodness is a classic Gestalt notion defined as salience or perceptual strength of a given pattern. All operational models of goodness have assigned a central role to mirror symmetry but not much attention has been paid to the distinction between global and local mirror symmetry, and their possible interactions. We designed eight different types of dot patterns (all consisting of 80 dots), combining different numbers (0, 1, and 2) and relative orientations (parallel or orthogonal to each other) of local and global axes of symmetry (affecting 50% or 100% of the dots, respectively) at different absolute orientations (vertical and horizontal). Each of 640 trials consisted of a short presentation of a new dot pattern, which subjects had to classify as regular or random. We hypothesised that the overall goodness of patterns is not the simple sum of the amount of regularity present in them but depends on the cooperation and competition between symmetries. The results confirmed our hypothesis, showing that performance in this regularity-detection task did not increase in a linear way when some symmetries were added to other symmetries.

scholarly journals EXCEPTIONAL STRING: INSTANTON EXPANSIONS AND SEIBERG–WITTEN CURVE

2002 ◽  
Vol 14 (09) ◽  
pp. 913-975 ◽  
Author(s):  
KENJI MOHRI
Keyword(s):  
Modular Forms ◽  
Mirror Symmetry ◽  
Elliptic Functions ◽  
Partition Functions ◽  
String Models ◽  
Local Mirror Symmetry

We investigate instanton expansions of partition functions of several toric E-string models using local mirror symmetry and elliptic modular forms. We also develop a method to determine the Seiberg–Witten curve of E-string with the help of elliptic functions.

scholarly journals Five-dimensional gauge theories and local mirror symmetry

2000 ◽  
Vol 586 (1-2) ◽  
pp. 331-345 ◽  
Author(s):  
Tohru Eguchi ◽  
Hiroaki Kanno
Keyword(s):  
Mirror Symmetry ◽  
Gauge Theories ◽  
Local Mirror Symmetry

scholarly journals Mirror symmetry for concavex vector bundles on projective spaces

2003 ◽  
Vol 2003 (3) ◽  
pp. 159-197 ◽  
Author(s):  
Artur Elezi
Keyword(s):  
Mirror Symmetry ◽  
Vector Bundles ◽  
Projective Spaces ◽  
Witten Theory ◽  
Generic Section ◽  
Projective Manifolds ◽  
Local Mirror Symmetry ◽  
Zero Locus

LetX⊂Ybe smooth, projective manifolds. Assume thatι:X→ℙsis the zero locus of a generic section ofV+=⊕i∈I𝒪(ki), where all theki's are positive. Assume furthermore that𝒩X/Y=ι∗(V−), whereV−=⊕j∈J𝒪(−lj)and all thelj's are negative. We show that under appropriate restrictions, the generalized Gromov-Witten invariants ofXinherited fromYcan be calculated via a modified Gromov-Witten theory onℙs. This leads to local mirror symmetry on theA-side.

scholarly journals A Generalized Construction of Calabi-Yau Models and Mirror Symmetry

2018 ◽  
Vol 4 (2) ◽  
Author(s):  
Per Berglund ◽  
Tristan Hubsch
Keyword(s):  
Sigma Models ◽  
General Class ◽  
Mirror Symmetry ◽  
Original Work ◽  
Convex Polytopes ◽  
Toric Varieties ◽  
Linear Sigma Models ◽  
Calabi Yau Manifolds

We extend the construction of Calabi-Yau manifolds to hypersurfaces in non-Fano toric varieties, requiring the use of certain Laurent defining polynomials, and explore the phases of the corresponding gauged linear sigma models. The associated non-reflexive and non-convex polytopes provide a generalization of Batyrev’s original work, allowing us to construct novel pairs of mirror models. We showcase our proposal for this generalization by examining Calabi-Yau hypersurfaces in Hirzebruch n-folds, focusing on n=3,4 sequences, and outline the more general class of so-defined geometries.

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