Determination of All General Homogeneous Polynomials Expressible as Determinants with Linear Elements

Emptiness of Homogeneous Linear Systems with Ten General Base Points

In this paper we give a new proof of the fact that for all pairs of positive integers (d, m) with d/m < 117/37, the linear system of plane curves of degree d with ten general base points of multiplicity m is empty.

Sampling of Homogeneous Polynomials

Conditions for reconstruction of multivariate homogeneous polynomials from sets of sample values are introduced, together with a frame-based method for explicitly obtaining the polynomial coefficients from the sample data.

Chain Queries Expressible by Linear Datalog Programs

Decomposition of Homogeneous Polynomials with Low Rank

Let F be a homogeneous polynomial of degree d in m+ 1 variables defined over an algebraically closed field of characteristic zero and suppose that F belongs to the s-th secant varieties of the standard Veronese variety Xm,d ⊂ P( m+d d )−1 but that its minimal decomposition as a sum of d-th powers of linear forms M1, . . . ,Mr is F = M 1 + · · · + M r with r > s. We show that if s + r ≤ 2d + 1 t...

Homogeneous Polynomials with Isomorphic Milnor Algebras

In this note we recall first Mather’s Lemma 2.4 providing effective necessary and sufficient conditions for a connected submanifold to be contained in an orbit. In Theorem 3.2 we show that two homogeneous polynomials f and g having isomorphic Milnor algebras are right-equivalent. This is similar to the celebrated theorem by Mather and Yau [4], saying that the isolated hypersurface singularities...