Some remarkable connections between commutative algebra and combinatorics have been
discovered in recent years. This book provides an overview of two of the main topics in this …

Abstract Let A= ⨁ _ i= 0^ c A_ i, A c≠ 0, be a graded Artinian algebra. We say that A has the
weak Lefschetz property (WLP) if there exists an element L∈ A 1 such that the multiplication …

Let A=⊕ i⩾ 0Ai be a standard graded Artinian K-algebra, where charK= 0. Then A has the
Weak Lefschetz property if there is an element ℓ of degree 1 such that the multiplication× ℓ …

The variety of sums of powers of a homogeneous polynomial of degree d in n variables is
de® ned and investigated in some examples, old and new. These varieties are studied via …

Lefschetz elements of Artinian Gorenstein algebras and Hessians of homogeneous polynomials
Page 1 Illinois Journal of Mathematics Volume 53, Number 2, Summer 2009, Pages 591–603 S …

We prove that the smallest degree of an apolar 0-dimensional scheme of a general cubic
form in n+ 1 variables is at most 2n+ 2, when n⩾ 8, and therefore smaller than the rank of the …

We review the open problems in the theory of deformations of zero-dimensional objects,
such as algebras, modules or tensors. We list both the well-known ones and some new ones …

We find the defining equations of Rees rings of linearly presented height three Gorenstein
ideals. To prove our main theorem we use local cohomology techniques to bound the …

We analyze the Gorenstein locus of the Hilbert scheme of d points on ℙ n ie, the open
subscheme parameterizing zero-dimensional Gorenstein subschemes of ℙ n of degree d …

Geometry and Algebra of Prime Fano 3-folds of Genus 12 Page 1 Geometry and Algebra of
Prime Fano 3-folds of Genus 12 FRANK-OLAF SCHREYER FakultÌt fu«r Mathematik und …