Given a set Γ of low-degree k-dimensional varieties in R[superscript n], we prove that for any D ⩾ 1, there is a non-zero polynomial P of degree at most D so that each component of R[superscript n]\Z(P) intersects O(D[superscript k−n]|Γ|) varieties of Γ
International audienceLet $F(x, y)∈C[x, y]$ be a polynomial of degreed and let $G(x, y)∈C[x, y]$ be ...
AbstractLet ƒ ∈ Q[y] be a polynomial of degree n over the rationals. Assume ƒ is indecomposable and ...
Abstract. We prove new bounds on the Betti numbers of real varieties and semi-algebraic sets that ha...
Abstract. We present a polynomial partitioning theorem for finite sets of points in the real locus o...
We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include ...
AbstractWe consider a family ofspolynomials, P = {P1, …,Ps}, inkvariables with coefficients in a rea...
Let Xn be an affine variety of dimension n and Yn be a quasi-projective variety of the same dimensio...
The purpose of this paper is to relate the variety parameterizing completely decomposable homogeneou...
AbstractFix an integral variety X⊂Pn, P∈Pn, and an integer k>0. Let S(X,P,k) be the set of all subse...
A recent extension of Guth (2015) to the basic polynomial partitioning technique of Guth and Katz (2...
Let K be a number field, Q, or the field of rational functions on a smooth projective curve of genus...
Given the space V of forms of degree d in n variables, and given an integer l >1and a partition ...
AbstractIn this paper an algorithm is described for the computation of the dimensions of all irreduc...
AbstractLet Dd,k denote the discriminant variety of degree d polynomials in one variable with at lea...
Let 3ίΓ be a finite field of characteristic p that contains exactly q elements. Let F(x) be a polyno...
International audienceLet $F(x, y)∈C[x, y]$ be a polynomial of degreed and let $G(x, y)∈C[x, y]$ be ...
AbstractLet ƒ ∈ Q[y] be a polynomial of degree n over the rationals. Assume ƒ is indecomposable and ...
Abstract. We prove new bounds on the Betti numbers of real varieties and semi-algebraic sets that ha...
Abstract. We present a polynomial partitioning theorem for finite sets of points in the real locus o...
We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include ...
AbstractWe consider a family ofspolynomials, P = {P1, …,Ps}, inkvariables with coefficients in a rea...
Let Xn be an affine variety of dimension n and Yn be a quasi-projective variety of the same dimensio...
The purpose of this paper is to relate the variety parameterizing completely decomposable homogeneou...
AbstractFix an integral variety X⊂Pn, P∈Pn, and an integer k>0. Let S(X,P,k) be the set of all subse...
A recent extension of Guth (2015) to the basic polynomial partitioning technique of Guth and Katz (2...
Let K be a number field, Q, or the field of rational functions on a smooth projective curve of genus...
Given the space V of forms of degree d in n variables, and given an integer l >1and a partition ...
AbstractIn this paper an algorithm is described for the computation of the dimensions of all irreduc...
AbstractLet Dd,k denote the discriminant variety of degree d polynomials in one variable with at lea...
Let 3ίΓ be a finite field of characteristic p that contains exactly q elements. Let F(x) be a polyno...
International audienceLet $F(x, y)∈C[x, y]$ be a polynomial of degreed and let $G(x, y)∈C[x, y]$ be ...
AbstractLet ƒ ∈ Q[y] be a polynomial of degree n over the rationals. Assume ƒ is indecomposable and ...
Abstract. We prove new bounds on the Betti numbers of real varieties and semi-algebraic sets that ha...
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