Related papers: Partial Differential Chow Forms and a Type of Part…
In this paper, the generic intersection theory for difference varieties is presented. Precisely, the intersection of an irreducible difference variety of dimension $d > 0$ and order $h$ with a generic difference hypersurface of order $s$ is…
In this paper, a generic intersection theorem in projective differential algebraic geometry is presented. Precisely, the intersection of an irreducible projective differential variety of dimension d>0 and order h with a generic projective…
In this paper, an intersection theory for generic differential polynomials is presented. The intersection of an irreducible differential variety of dimension $d$ and order $h$ with a generic differential hypersurface of order $s$ is shown…
Chow varieties are a parameter space for cycles of a given variety of a given codimension and degree. We construct their analog for differential algebraic varieties with differential algebraic subvarieties, answering a question of Gao, Li…
For a quasiprojective variety S, we define a category CHM(S) of pure Chow motives over S. Assuming conjectures of Grothendieck and Murre, we show that the decomposition theorem holds in CHM(S). As a consequence, the intersection complex of…
We study intersection theory for differential algebraic varieties. Particularly, we study families of differential hypersurface sections of arbitrary affine differential algebraic varieties over a differential field. We prove the…
We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…
We present a bounded probability algorithm for the computation of the Chow forms of the equidimensional components of an algebraic variety. Its complexity is polynomial in the length and in the geometric degree of the input equation system…
This paper deals with properties of the algebraic variety defined as the set of zeros of a "deficient" sequence of multivariate polynomials. We consider two types of varieties: ideal-theoretic complete intersections and absolutely…
We study intersection theory and Chern classes of reflexive sheaves on normal varieties. In particular, we define generalization of Mumford's intersection theory on normal surfaces to higher dimensions. We also define and study the second…
The Hurwitz form of a projective variety characterizes linear spaces of complementary dimension which meet the variety non-transversally. We extend this notion to varieties in a product of projective spaces. This parallels the multigraded…
A presentation of a degree $d$ form in $n+1$ variables as the sum of homogenous elements ``essentially'' involving $n$ variables is called a {\em codimension one decomposition}. Codimension one decompositions are introduced and the related…
Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi--orthogonality conditions. We obtain several characterizations for these…
The study of Chow varieties of decomposable forms lies at the confluence of algebraic geometry, commutative algebra, representation theory and combinatorics. There are many open questions about homological properties of Chow varieties and…
We find a new presentation of the stack of hyperelliptic curves of odd genus as a quotient stack and we use it to compute its integral Chow ring by means of equivariant intersection theory.
The Chow variety of polynomials that decompose as a product of linear forms has been studied for more than 100 years. Finding equations in the ideal of secant varieties of Chow varieties would enable one to measure the complexity the…
A differential version of the classical Weil descent is established in all characteristics. It yields a theory of differential restriction of scalars for differential varieties over finite differential field extensions. This theory is then…
In this paper we generalize the Ritt-Kolchin method of characteristic sets and the classical Gr\"obner basis technique to prove the existence and obtain methods of computation of multivariate difference-differential dimension polynomials…
A theorem of Chow concerns homomorphisms of two abelian varieties under a primary field extension base change. In this paper we generalize Chow's theorem to semi-abelian varieties. This contributes to different proofs of a well-known result…
In this paper we study the problem of computing a Kolchin characteristic set of a radical differential ideal. The central part of the article is the presentation of algorithms solving this problem in two principal cases: for ordinary…