Ehrhart polynomials of convex polytopes, ℎ-vectors of simplicial complexes, and nonsingular projective toric varieties

1991 ◽  
pp. 165-178 ◽  
Author(s):  
Takayuki Hibi
Keyword(s):  
Convex Polytopes ◽  
Toric Varieties ◽  
Simplicial Complexes ◽  
Ehrhart Polynomials

scholarly journals Secant varieties of toric varieties arising from simplicial complexes

2020 ◽  
Vol 588 ◽  
pp. 428-457
Author(s):  
M. Azeem Khadam ◽  
Mateusz Michałek ◽  
Piotr Zwiernik
Keyword(s):  
Toric Varieties ◽  
Simplicial Complexes ◽  
Secant Varieties

scholarly journals Ehrhart polynomials of convex polytopes with small volumes

2011 ◽  
Vol 32 (2) ◽  
pp. 226-232 ◽  
Author(s):  
Takayuki Hibi ◽  
Akihiro Higashitani ◽  
Yuuki Nagazawa
Keyword(s):  
Convex Polytopes ◽  
Ehrhart Polynomials

scholarly journals Matchings in simplicial complexes, circuits and toric varieties

2007 ◽  
Vol 114 (2) ◽  
pp. 300-310 ◽  
Author(s):  
Anargyros Katsabekis ◽  
Apostolos Thoma
Keyword(s):  
Toric Varieties ◽  
Simplicial Complexes

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.

Combinatorial Invariance of Stanley–Reisner Rings

1996 ◽  
Vol 3 (4) ◽  
pp. 315-318
Author(s):  
W. Bruns ◽  
J. Gubeladze
Keyword(s):  
Convex Polytopes ◽  
Short Note ◽  
Simplicial Complexes ◽  
Algebraic Combinatorics ◽  
Rigidity Property

Abstract In this short note we show that Stanley–Reisner rings of simplicial complexes, which have had a “dramatic application” in combinatorics [Hibi, Algebraic Combinatorics on Convex Polytopes, Carslaw Publications, 1992, p. 41], possess a rigidity property in the sense that they determine their underlying simplicial complexes.

scholarly journals Infinite families of equivariantly formal toric orbifolds

2019 ◽  
Vol 31 (2) ◽  
pp. 283-301
Author(s):  
Anthony Bahri ◽  
Soumen Sarkar ◽  
Jongbaek Song
Keyword(s):  
Cohomology Ring ◽  
Toric Varieties ◽  
Simplicial Complexes ◽  
Simple Polytopes ◽  
Toric Manifolds ◽  
Integral Cohomology

AbstractThe simplicial wedge construction on simplicial complexes and simple polytopes has been used by a variety of authors to study toric and related spaces, including non-singular toric varieties, toric manifolds, intersections of quadrics and more generally, polyhedral products. In this paper we extend the analysis to include toric orbifolds. Our main results yield infinite families of toric orbifolds, derived from a given one, whose integral cohomology is free of torsion and is concentrated in even degrees, a property which might be termed integrally equivariantly formal. In all cases, it is possible to give a description of the cohomology ring and to relate it to the cohomology of the original orbifold.

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