The hypersurfaces of degree d in the projective space P n correspond to points of P N , where N = n+d d âˆ’ 1. Now assume d = 2e is even, and let X (n,d) âŠ† P N denote the subvariety of two e-foldâ€¦ (More)

We reconsider the classical problem of representing a finite number of forms of degree d in the polynomial ring over n + 1 variables as scalar combinations of powers of linear forms. We define aâ€¦ (More)

We describe the tangent space to the parameter variety of all artin level quotients of a polynomial ring in n variables having specified socle degree and type. When n = 2, we relate this variety toâ€¦ (More)

We revisit an old problem in classical invariant theory, viz. that of giving algebraic conditions for a binary form to have linear factors with assigned multiplicities. We construct a complex ofâ€¦ (More)

Cubic forms in three variables are parametrised by points of a projec-tive space P 9. We study the subvarieties in this space defined by de-composable forms. Specifically, we calculate theirâ€¦ (More)

Given integers n, d, e with 1 â‰¤ e < d2 , let X âŠ† P ( d )âˆ’1 denote the locus of degree d hypersurfaces in P which are supported on two hyperplanes with multiplicities dâˆ’ e and e. Thus X is theâ€¦ (More)

Let H âŠ† P5 denote the hypersurface of binary quintics in involution, with defining equation given by the Hermite invariant H. In Â§2 we find the singular locus of H, and show that it is a completeâ€¦ (More)

Let A, B denote binary forms of order d, and let C 2râˆ’1 = (A, B) 2râˆ’1 be the sequence of their linear combinants for 1 â‰¤ r â‰¤ âŒŠ d+1 2 âŒ‹. It is known that C 1 , C 3 together determine the pencil {A+Î»â€¦ (More)

For generic binary forms A1, . . . , Ar of order d we construct a class of combinants C = {Cq : 0 â‰¤ q â‰¤ r, q 6= 1}, to be called the Wronskian combinants of the Ai. We show that the collection Câ€¦ (More)