Intersection theory in differential algebraic geometry: Generic intersections and the differential Chow form

Intersection Theory in Differential Algebraic Geometry: Generic Intersections and the Differential Chow Form

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 to be an irreducible variety of dimension d − 1 and order h + s. As a consequence, the dimension conjecture for generic differential polynomials is proved. Based on...

Intersection Theory for Generic Differential Polynomials and Differential Chow Form

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 to be an irreducible variety of dimension d − 1 and order h + s. As a consequence, the dimension conjecture for generic differential polynomials is proved. Based on...

Differential Chow Form for Projective Differential Variety

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 differential hyperplane is shown to be an irreducible projective differential variety of dimension d − 1 and order h. Based on the generic intersection theo...

Model Theory and Differential Algebraic Geometry

Differential Algebraic Formulation of Normal Form Theory

A differential algebraic (DA) formulation of a normal form theory for repetitive systems is presented. Contrary to previous approaches, no Lie algebraic tools are used. The resulting algorithm is very transparent and not restricted to the treatment of symplectic systems. In the case of symplectic systems, the normal form algorithm provides a nonlinear coordinate transformation in which the moti...