The secondary polytope

2006 ◽  
pp. 73-83
Author(s):  
Rekha Thomas
Keyword(s):  
Secondary Polytope

Secondary Polytope and Secondary Power Diagram

2019 ◽  
Vol 59 (12) ◽  
pp. 2045-2045
Author(s):  
Na Lei ◽  
Wei Chen ◽  
Zhongxuan Luo ◽  
Hang Si ◽  
Xianfeng Gu
Keyword(s):  
Power Diagram ◽  
Secondary Polytope ◽  
Secondary Power

Secondary Polytope and Secondary Power Diagram

2019 ◽  
Vol 59 (12) ◽  
pp. 1965-1981
Author(s):  
Na Lei ◽  
Wei Chen ◽  
Zhongxuan Luo ◽  
Hang Si ◽  
Xianfeng Gu
Keyword(s):  
Power Diagram ◽  
Secondary Polytope ◽  
Secondary Power

scholarly journals The KSBA compactification of the moduli space of $$D_{1,6}$$-polarized Enriques surfaces

2021 ◽  
Author(s):  
Luca Schaffler
Keyword(s):  
Finite Group ◽  
Moduli Space ◽  
Blow Up ◽  
Unit Cube ◽  
Finite Group Action ◽  
Stable Pair ◽  
Enriques Surfaces ◽  
Secondary Polytope ◽  
Stable Pairs ◽  
A Finite Group

AbstractWe describe a compactification by stable pairs (also known as KSBA compactification) of the 4-dimensional family of Enriques surfaces which arise as the $${\mathbb {Z}}_2^2$$ Z 2 2 -covers of the blow up of $${\mathbb {P}}^2$$ P 2 at three general points branched along a configuration of three pairs of lines. Up to a finite group action, we show that this compactification is isomorphic to the toric variety associated to the secondary polytope of the unit cube. We relate the KSBA compactification considered to the Baily–Borel compactification of the same family of Enriques surfaces. Part of the KSBA boundary has a toroidal behavior, another part is isomorphic to the Baily–Borel compactification, and what remains is a mixture of these two. We relate the stable pair compactification studied here with Looijenga’s semitoric compactifications.

ENUMERATING TRIANGULATIONS IN GENERAL DIMENSIONS

2002 ◽  
Vol 12 (06) ◽  
pp. 455-480 ◽  
Author(s):  
HIROSHI IMAI ◽  
TOMONARI MASADA ◽  
FUMIHIKO TAKEUCHI ◽  
KEIKO IMAI
Keyword(s):  
Independent Set ◽  
Equivalence Classes ◽  
Maximal Independent Set ◽  
Search Technique ◽  
Enumeration Algorithm ◽  
General Dimension ◽  
Secondary Polytope ◽  
With Memory

We propose algorithms to enumerate (1) regular triangulations, (2) spanning regular triangulations, (3) equivalence classes of regular triangulations with respect to symmetry, and (4) all triangulations. All of the algorithms are for arbitrary points in general dimension. They work in output-size sensitive time with memory only of several times the size of a triangulation. For the enumeration of regular triangulations, we use the fact by Gel'fand, Zelevinskii and Kapranov that regular triangulations correspond to the vertices of the secondary polytope. We use reverse search technique by Avis and Fukuda, its extension for enumerating equivalence classes of objects, and a reformulation of a maximal independent set enumeration algorithm. The last approach can be extended for enumeration of dissections.

scholarly journals The moduli space of Harnack curves in toric surfaces

2021 ◽  
Vol 9 ◽  
Author(s):  
Jorge Alberto Olarte
Keyword(s):  
Moduli Space ◽  
Newton Polygon ◽  
Lattice Points ◽  
Toric Surface ◽  
Toric Surfaces ◽  
Tropical Curves ◽  
Secondary Polytope

Abstract In 2006, Kenyon and Okounkov Kenyon and Okounkov [12] computed the moduli space of Harnack curves of degree d in ${\mathbb {C}\mathbb {P}}^2$ . We generalise their construction to any projective toric surface and show that the moduli space ${\mathcal {H}_\Delta }$ of Harnack curves with Newton polygon $\Delta $ is diffeomorphic to ${\mathbb {R}}^{m-3}\times {\mathbb {R}}_{\geq 0}^{n+g-m}$ , where $\Delta $ has m edges, g interior lattice points and n boundary lattice points. This solves a conjecture of Crétois and Lang. The main result uses abstract tropical curves to construct a compactification of this moduli space where additional points correspond to collections of curves that can be patchworked together to produce a curve in ${\mathcal {H}_\Delta }$ . This compactification has a natural stratification with the same poset as the secondary polytope of $\Delta $ .

Secondary Power Diagram, Dual of Secondary Polytope

2019 ◽  
pp. 3-24
Author(s):  
Na Lei ◽  
Wei Chen ◽  
Zhongxuan Luo ◽  
Hang Si ◽  
Xianfeng Gu
Keyword(s):  
Power Diagram ◽  
Secondary Polytope ◽  
Secondary Power

scholarly journals On the facets of the secondary polytope

2011 ◽  
Vol 118 (2) ◽  
pp. 425-447 ◽  
Author(s):  
Sven Herrmann
Keyword(s):  
Secondary Polytope
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