The Viro method for construction of Bernstein-Bézier algebraic hypersurface piece

2012 ◽  
Vol 55 (6) ◽  
pp. 1269-1279 ◽  
Author(s):  
YiSheng Lai ◽  
WeiPing Du ◽  
RenHong Wang
Keyword(s):  
Algebraic Hypersurface ◽  
Viro Method

scholarly journals The Viro Method for Construction of Piecewise Algebraic Hypersurfaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yisheng Lai ◽  
Weiping Du ◽  
Renhong Wang
Keyword(s):  
New Method ◽  
Algebraic Hypersurface ◽  
And Topology ◽  
Algebraic Hypersurfaces ◽  
Viro Method

We propose a new method to construct a real piecewise algebraic hypersurface of a given degree with a prescribed smoothness and topology. The method is based on the smooth blending theory and the Viro method for construction of Bernstein-Bézier algebraic hypersurface piece on a simplex.

scholarly journals Amoeba-Shaped Polyhedral Complex of an Algebraic Hypersurface

2018 ◽  
Vol 29 (2) ◽  
pp. 1356-1368 ◽  
Author(s):  
Mounir Nisse ◽  
Timur Sadykov
Keyword(s):  
Polyhedral Complex ◽  
Algebraic Hypersurface

scholarly journals Zero Counting and Invariant Sets of Differential Equations

2017 ◽  
Vol 2019 (13) ◽  
pp. 4119-4158
Author(s):  
Gal Binyamini
Keyword(s):  
Vector Field ◽  
Differential Equations ◽  
Upper Bound ◽  
Linear Differential Equations ◽  
Invariant Sets ◽  
Polynomial Vector ◽  
Algebraic Hypersurface ◽  
Polynomial Differential Equations ◽  
Polynomial Vector Field ◽  
Linear Differential

Abstract Consider a polynomial vector field $\xi$ in ${\mathbb C}^n$ with algebraic coefficients, and $K$ a compact piece of a trajectory. Let $N(K,d)$ denote the maximal number of isolated intersections between $K$ and an algebraic hypersurface of degree $d$. We introduce a condition on $\xi$ called constructible orbits and show that under this condition $N(K,d)$ grows polynomially with $d$. We establish the constructible orbits condition for linear differential equations over ${\mathbb C}(t)$, for planar polynomial differential equations and for some differential equations related to the automorphic $j$-function. As an application of the main result, we prove a polylogarithmic upper bound for the number of rational points of a given height in planar projections of $K$ following works of Bombieri–Pila and Masser.

scholarly journals Euler characteristic of primitiveT-hypersurfaces and maximal surfaces

2009 ◽  
Vol 9 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Benoit Bertrand
Keyword(s):  
Euler Characteristic ◽  
Tropical Geometry ◽  
Toric Varieties ◽  
Three Dimensional ◽  
Maximal Surfaces ◽  
The Real ◽  
Complex Part ◽  
Algebraic Hypersurfaces ◽  
Viro Method

AbstractViro method plays an important role in the study of topology of real algebraic hypersurfaces. TheT-primitive hypersurfaces we study here appear as the result of Viro's combinatorial patchworking when one starts with a primitive triangulation. We show that the Euler characteristic of the real part of such a hypersurface of even dimension is equal to the signature of its complex part. We explain how this can be understood in tropical geometry. We use this result to prove the existence of maximal surfaces in some three-dimensional toric varieties, namely those corresponding to Nakajima polytopes.

Localization of an algebraic hypersurface by the exclusion algorithm

1992 ◽  
Vol 2 (4) ◽  
pp. 239-256 ◽  
Author(s):  
Jean-Pierre Dedieu ◽  
Jean-Claude Yakoubsohn
Keyword(s):  
Algebraic Hypersurface
Sign in / Sign up

Export Citation Format

Share Document