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Recent developments in toric geometry
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A survey of recent developments in the theory of toric varieties can be found in this article, including new constructions of Toric varieties and relations to symplectic geometry, combinatorics and mirror symmetry.Abstract:
This paper will appear in the Proceedings of the 1995 Santa Cruz Summer Institute. The paper is a survey of recent developments in the theory of toric varieties, including new constructions of toric varieties and relations to symplectic geometry, combinatorics and mirror symmetry.read more
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MonographDOI
Torus Actions and their Applications in Topology and Combinatorics
TL;DR: Polytopes topology and combinatorics of simplicial complexes Commutative and homological algebra of Cubical complexes Cubical Complexes Toric and quasitoric manifolds Moment-angle Complexes Cohomology of moment-angle complexes as discussed by the authors.
Book
Moment Maps, Cobordisms, and Hamiltonian Group Actions
TL;DR: In this article, the Kawasaki Riemann-Roch formula was used to prove the Hamiltonian cobordism invariance of the index of a transversally elliptic operator.
Journal ArticleDOI
PALP: A Package for Analysing Lattice Polytopes with applications to toric geometry☆
Maximilian Kreuzer,Harald Skarke +1 more
TL;DR: The package PALP of C programs for calculations with lattice polytopes and applications to toric geometry, which is freely available on the internet, contains routines for vertex and facet enumeration, computation of incidences and symmetries, as well as completion of the set of lattice points in the convex hull of a given set of points.
Journal ArticleDOI
Topological string amplitudes, complete intersection Calabi-Yau spaces and threshold corrections
TL;DR: In this paper, the authors present the most complete list of mirror pairs of Calabi-Yau complete intersections in toric ambient varieties and develop the methods to solve the topological string and to calculate higher genus amplitudes on these compact CalabiYau spaces.
Posted Content
D-branes on Stringy Calabi-Yau Manifolds
TL;DR: In this paper, it was shown that fractional branes corresponding to rational B boundary states in a Gepner model can be seen as fractional BRs in the Landau-Ginzburg orbifold phase of the linear sigma model description.
References
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Book
Introduction to Toric Varieties.
TL;DR: In this article, a mini-course is presented to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications, concluding with Stanley's theorem characterizing the number of simplicies in each dimension in a convex simplicial polytope.
Journal ArticleDOI
Phases of N = 2 theories in two dimensions
TL;DR: In this paper, a natural relation between sigma models based on Calabi-Yau hypersurfaces in weighted projective spaces and Landau-Ginzburg models is found.
Journal ArticleDOI
A Pair of Calabi-Yau manifolds as an exactly soluble superconformal theory
TL;DR: In this paper, the prepotentials and geometry of the moduli spaces for a Calabi-Yau manifold and its mirror were derived and all the sigma model corrections to the Yukawa couplings and moduli space metric were obtained.
Book ChapterDOI
Homological Algebra of Mirror Symmetry
TL;DR: Mirror symmetry was discovered several years ago in string theory as a duality between families of 3-dimensional Calabi-Yau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeros).
Journal Article
Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties
TL;DR: In this article, it was shown that there exists an isomorphism between two conformal field theories corresponding to Calabi-Yau varieties from two families of algebraic compactifications of affine hypersurfaces.