PALP: A Package for Analyzing Lattice Polytopes with Applications to Toric Geometry
arXiv:math/0204356 · doi:10.1016/S0010-4655(03)00491-0
Abstract
We describe our package PALP of C programs for calculations with lattice polytopes and applications to toric geometry, which is freely available on the internet. It 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. In addition, there are procedures specialised to reflexive polytopes such as the enumeration of reflexive subpolytopes, and applications to toric geometry and string theory, like the computation of Hodge data and fibration structures for toric Calabi-Yau varieties. The package is well tested and optimised in speed as it was used for time consuming tasks such as the classification of reflexive polyhedra in 4 dimensions and the creation and manipulation of very large lists of 5-dimensional polyhedra. While originally intended for low-dimensional applications, the algorithms work in any dimension and our key routine for vertex and facet enumeration compares well with existing packages.
Latex2e, 22 pages
References in corpus (21)
- Evidence for F-Theory
- Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
- K3--Fibrations and Heterotic-Type II String Duality
- On the Ubiquity of K3 Fibrations in String Duality
- Duality Between the Webs of Heterotic and Type II Vacua
- Dual Cones and Mirror Symmetry for Generalized Calabi-Yau Manifolds
- On the Classification of Quasihomogeneous Functions
- On the Classification of Reflexive Polyhedra
- Landau-Ginzburg String Vacua
- No Mirror Symmetry in Landau-Ginzburg Spectra!
- Searching for K3 Fibrations
- Complete classification of reflexive polyhedra in four dimensions
- Landau-Ginzburg Vacua of String, M- and F-Theory at c=12
- Weight systems for toric Calabi-Yau varieties and reflexivity of Newton polyhedra
- All Abelian Symmetries of Landau-Ginzburg Potentials
- Toric complete intersections and weighted projective space
- Landau-Ginzburg orbifolds with discrete torsion
- ADE string vacua with discrete torsion
- Strings on Calabi--Yau spaces and Toric Geometry
- Toric morphisms and fibrations of toric Calabi-Yau hypersurfaces
- ON THE EXTENDED POINCARE POLYNOMIAL
Cited by in corpus (112)
- Flux Compactification
- Tensionless Strings and the Weak Gravity Conjecture
- Global F-theory GUTs
- A Stringy Test of the Scalar Weak Gravity Conjecture
- Two Hundred Heterotic Standard Models on Smooth Calabi-Yau Threefolds
- D-Branes at del Pezzo Singularities: Global Embedding and Moduli Stabilisation
- Explicit de Sitter Flux Vacua for Global String Models with Chiral Matter
- F-Theory GUT Vacua on Compact Calabi-Yau Fourfolds
- The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces
- Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections
- A Calabi-Yau Database: Threefolds Constructed from the Kreuzer-Skarke List
- Building an explicit de Sitter
- On Free Quotients of Complete Intersection Calabi-Yau Manifolds
- Moduli Stabilisation for Chiral Global Models
- Gorenstein toric Fano varieties
- Canonical toric Fano threefolds
- Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space
- On the Hodge structure of elliptically fibered Calabi-Yau threefolds
- Toric K3-Fibred Calabi-Yau Manifolds with del Pezzo Divisors for String Compactifications
- Topological Invariants and Fibration Structure of Complete Intersection Calabi-Yau Four-Folds
- A New Construction of Calabi-Yau Manifolds: Generalized CICYs
- A Systematic Approach to Kähler Moduli Stabilisation
- Four-modulus "Swiss Cheese" chiral models
- On Classifying the Divisor Involutions in Calabi-Yau Threefolds
- Toric Construction of Global F-Theory GUTs
- Global SO(10) F-theory GUTs
- Heterotic Models from Vector Bundles on Toric Calabi-Yau Manifolds
- Integral Cohomology and Mirror Symmetry for Calabi-Yau 3-folds
- Complete toric varieties with reductive automorphism group
- The Vertical, the Horizontal and the Rest: anatomy of the middle cohomology of Calabi-Yau fourfolds and F-theory applications
- Heavy Tails in Calabi-Yau Moduli Spaces
- K-polystability of Q-Fano varieties admitting Kahler-Einstein metrics
- Worldsheet Instantons and Torsion Curves, Part B: Mirror Symmetry
- Counting String Theory Standard Models
- The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning
- Computing symmetry groups of polyhedra
- Toric complete intersections and weighted projective space
- Multiple Fibrations in Calabi-Yau Geometry and String Dualities
- Toric Elliptic Fibrations and F-Theory Compactifications
- Calabi-Yau Duals of Torus Orientifolds
- A Three-Generation Calabi-Yau Manifold with Small Hodge Numbers
- Worldsheet Instantons and Torsion Curves, Part A: Direct Computation
- Computational Tools for Cohomology of Toric Varieties
- Estimating Calabi-Yau Hypersurface and Triangulation Counts with Equation Learners
- Traintrack Calabi-Yaus from Twistor Geometry
- PALP - a User Manual
- (0,2) Deformations of Linear Sigma Models
- Toric Methods in F-theory Model Building
- Flux compactification on smooth, compact three-dimensional toric varieties
- Calabi-Yau Volumes and Reflexive Polytopes
- Hyperconifold Transitions, Mirror Symmetry, and String Theory
- Effective action from M-theory on twisted connected sum -manifolds
- New Calabi-Yau Manifolds from Genetic Algorithms
- An Analysis of Fluxes by Duality
- Global embeddings for branes at toric singularities
- Heterotic Bundles on Calabi-Yau Manifolds with Small Picard Number
- All Weight Systems for Calabi-Yau Fourfolds from Reflexive Polyhedra
- Four Kahler Moduli Stabilisation in type IIB Orientifolds with K3-fibred Calabi-Yau threefold compactification
- Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties
- Applying machine learning to the Calabi-Yau orientifolds with string vacua
- Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges
- Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions
- Deforming, revolving and resolving - New paths in the string theory landscape
- F-theory duals of singular heterotic K3 mode
- D-brane central charge and Landau-Ginzburg orbifolds
- On K3-fibred LARGE Volume Scenario with de Sitter vacua from anti-D3-branes
- Landscape Study of Target Space Duality of (0,2) Heterotic String Models
- A new offspring of PALP
- F-theory and Heterotic Duality, Weierstrass Models from Wilson lines
- Triadophilia: A Special Corner in the Landscape
- A pair of Calabi-Yau manifolds from a two parameter non-Abelian gauged linear sigma model
- The 14th case VHS via K3 fibrations
- New Examples of Compact Manifolds with Holonomy Spin(7)
- Classifying divisor topologies for string phenomenology
- Seeking de-Sitter Vacua in the String Landscape
- Classification of toric Fano 5-folds
- Patterns in Calabi-Yau Distributions
- On genus one fibered Calabi-Yau threefolds with 5-sections
- Heterotic flux backgrounds and their IIA duals
- Universes as Big Data
- On Fano threefolds with canonical Gorenstein singularities
- Probing Geometry with Stability Conditions
- Projecting Fanos in the mirror
- Machine learning the dimension of a Fano variety
- Chern-Simons Invariants and Heterotic Superpotentials
- The making of Calabi-Yau spaces: Beyond toric hypersurfaces
- Heterotic (0,2) Gepner Models and Related Geometries
- Normal forms of convex lattice polytopes
- Fano hypersurfaces and Calabi-Yau supermanifolds
- On the Statistics of Lattice Polytopes
- Constructing new Calabi-Yau 3-folds and their mirrors via conifold transitions
- Futaki Invariants and Reflexive Polygons
- Counting Points and Hilbert Series in String Theory
- Small toric degenerations of Fano threefolds
- Complete Intersection Fibers in F-Theory
- On the quantum homology algebra of toric Fano manifolds
- Heterotic strings on and their dual Calabi-Yau threefolds
- Calabi-Yau Four/Five/Six-folds as Hypersurfaces: Machine Learning, Approximation, and Generation
- Quiver Gauge Theories: Beyond Reflexivity
- Wavefunctions on magnetized branes in the conifold
- Target Space Dualities of Heterotic Grand Unified Theories
- Max Kreuzer's Contributions to the Study of Calabi-Yau Manifolds
- Early Universe Cosmology, Effective Supergravity, and Invariants of Algebraic Forms
- Two One-Parameter Special Geometries
- Modularity of Landau-Ginzburg models
- An N=1 Triality by Spectrum Matching
- The reflexive dimension of a lattice polytope
- Large N Duality for Compact Calabi-Yau Threefolds
- Deformations of equivelar Stanley-Reisner abelian surfaces
- Classification of width 1 lattice tetrahedra by their multi-width
- Combinatorics in N = 1 Heterotic Vacua
- Fano threefolds with canonical Gorenstein singularities and big degree