Determinantal variety and normal embedding

Normal and Triangular Determinantal Representations of Multivariate Polynomials

In this paper we give a new and simple algorithm to put any multivariate polynomial into a normal determinant form in which each entry has the form i i i b x a  , and in each column the same variable appears. We also apply the algorithm to obtain a triangular determinant representation, a reduced determinant representation, and a uniform determinant representation of any multivariable polynomi...

Embedding of a Maximal Curve in a Hermitian Variety

Let X be a projective geometrically irreducible non-singular algebraic curve defined over a finite field Fq2 of order q . If the number of Fq2 -rational points of X satisfies the Hasse-Weil upper bound, then X is said to be Fq2 -maximal. For a point P0 ∈ X (Fq2 ), let π be the morphism arising from the linear series D := |(q + 1)P0|, and let N := dim(D). It is known that N ≥ 2 and that π is ind...

Producing Good Quotients by Embedding into a Toric Variety

Normal Self-intersections of the Characteristic Variety

Let P = PtP2 + 2 be a linear partial differential operator on R^ with Pt and P2, of orders mx and ra2, respectively, strictly hyperbolic with respect to the first variable and Q of order ml + m2 2. Although the characteristic variety of P may have self-intersections, the hyperbolicity of Px and P2 implies local solvability for Pu = ƒ; indeed the Cauchy problem for P is locally solvable. In this...

Krs and Determinantal Ideals