scholarly journals Elliptic genera of toric varieties and applications to mirror symmetry

2000 ◽  
Vol 140 (2) ◽  
pp. 453-485 ◽  
Author(s):  
Lev A. Borisov ◽  
Anatoly Libgober
Keyword(s):  
Mirror Symmetry ◽  
Toric Varieties ◽  
Elliptic Genera

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 ELLIPTIC GENERA, TORUS ORBIFOLDS AND MULTI-FANS II

2006 ◽  
Vol 17 (06) ◽  
pp. 707-735 ◽  
Author(s):  
AKIO HATTORI
Keyword(s):  
Toric Varieties ◽  
Elliptic Genus ◽  
Elliptic Genera ◽  
Rigidity Theorems

Rigidity theorems for orbifold elliptic genus of complete simplicial multi-fans are formulated and proved. Applications to n-dimesional Q-factorial toric varieties whose canonical divisors are divisible by n are given.

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.

scholarly journals T-duality and homological mirror symmetry for toric varieties

2012 ◽  
Vol 229 (3) ◽  
pp. 1873-1911 ◽  
Author(s):  
Bohan Fang ◽  
Chiu-Chu Melissa Liu ◽  
David Treumann ◽  
Eric Zaslow
Keyword(s):  
Mirror Symmetry ◽  
Toric Varieties ◽  
Homological Mirror Symmetry

scholarly journals Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces

2016 ◽  
Vol 123 (1) ◽  
pp. 199-282 ◽  
Author(s):  
Mohammed Abouzaid ◽  
Denis Auroux ◽  
Ludmil Katzarkov
Keyword(s):  
Mirror Symmetry ◽  
Toric Varieties

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 Mirror symmetry and the moduli space for generic hypersurfaces in toric varieties

1995 ◽  
Vol 456 (1-2) ◽  
pp. 153-204 ◽  
Author(s):  
Per Berglund ◽  
Sheldon Katz ◽  
Albrecht Klemm
Keyword(s):  
Moduli Space ◽  
Mirror Symmetry ◽  
Toric Varieties
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