Hibi T. Algebraic and Geometric Combinatorics on Lattice Polytopes 2018

Textbook in PDF format

Preface
Introduction to toric geometry with a view towards lattice polytopes
A brief introduction to valuations on lattice polytopes
Ehrhart positivity and Demazure characters
Families of 3-dimensional polytopes of mixed degree one
Some lattice parallelepipeds with unimodular covers
A brief survey on lattice zonotopes
A pithy look at the polytope algebra
Restrictions on the singularity content of a Fano polygon
Finding a fully mixed cell in a mixed subdivision of polytopes
Predicting the integer decomposition property via machine learning
Lattice polytopes in mathematical physics
A brief survey about moment polytopes of subvarieties of products of Grassmanians
Cubical Dehn–Sommerville equations and self-reciprocal cubical complexes
Hollow lattice polytopes: Latest advances in classification and relations with the width
The Lecture Hall cone as a toric deformation
A short survey on Tesler matrices and Tesler polytopes
Eberhard-type theorems with two kinds of polygons
Complete intersection Calabi–Yau threefolds in Hibi toric varieties and their smoothing
Technically, squares are polytopes
On local Dressians of matroids
Polyhedral geometry for lecture hall partitions
A note on deformations and mutations of fake weighted projective planes
Special cases and a dual view on the local formulas for Ehrhart coefficients from lattice tiles
Local h*-polynomials of some weighted projective spaces
On the faces of simple polytopes
Notes on toric Fano varieties associated to building sets
A Reider-type result for smooth projective toric surfaces
Face enumeration on flag complexes and flag spheres
Open problems from the 2018 Summer Workshop on Lattice Polytopes at Osaka University
Author index