Sylvester versus Gundelfinger

Sylvester versus Gundelfinger

Let Vn be the SL2-module of binary forms of degree n and let V = V1 ⊕ V3 ⊕ V4. We show that the minimum number of generators of the algebra R = C[V ]2 of polynomial functions on V invariant under the action of SL2 equals 63. This settles a 142-year old question.

The Sylvester-Chvatal Theorem

The Sylvester-Gallai theorem asserts that every finite set S of points in two-dimensional Euclidean space includes two points, a and b, such that either there is no other point in S is on the line ab, or the line ab contains all the points in S. V. Chvátal extended the notion of lines to arbitrary metric spaces and made a conjecture that generalizes the Sylvester-Gallai theorem. In the present ...

Rectangular Corner Cutting Sylvester

This paper presents a way to construct the Sylvester A-resultant matrix for three bi-degree (m; n) polynomials whose exponent set is cut oo by rectangles at the corners. The paper also shows that the determinant of this matrix does give the resultant of the three polynomials.

Sylvester ' S Mathematical Papers

Fractional Sylvester-Gallai Theorems∗

We prove fractional analogs of the classical Sylvester-Gallai theorem. Our theorems translate local information about collinear triples in a set of points into global bounds on the dimension of the set. Specifically, we show that if for every points v in a finite set V ⊂ C, there are at least δ|V | other points u ∈ V for which the line through v, u contains a third point in V , then V resides i...