If M is the complement of a hyperplane arrangement, and A = H∗(M, k) is the cohomology ring of M over a field k of characteristic 0, then the ranks, φk, of the lower central series quotients of π1(M)… (More)

In [2], Billera proved that theR-algebra of continuous piecewise polynomial functions (C0 splines) on ad-dimensional simplicial complex1 embedded inRd is a quotient of the Stanley–Reisner ring A1 of… (More)

We have previously shown that methionine can be used as a “switchable” residue for the design of peptides with alternative secondary structure preferences in the aggregated state ( J. Am.Chem. Soc.… (More)

If A is a complex hyperplane arrangement, with complement X, we show that the Chen ranks of G = π1(X) are equal to the graded Betti numbers of the linear strand in a minimal, free resolution of the… (More)

Associated to a projective arrangement of hyperplanes A ⊆ P n is the module D(A), which consists of derivations tangent to A. We study D(A) when A is a configuration of lines in P 2. In this setting,… (More)

We study the Hilbert series of a family of ideals J φ generated by powers of linear forms in K[x1,. .. , xn]. Using the results of Emsalem-Iarrobino, we formulate this as a question about fatpoints… (More)

For a simplicial subdivison of a region inkn (k algebraically closed) and r ∈ N, there is a reflexive sheaf K onPn, such thatH0(K(d)) is essentially the space of piecewise polynomial functions on ,… (More)

gezogen, ulld bei anderen Schnecken ist neuerdings die Fruchtbarkeit solcher isoliert aufgezogener Exemplare konstatiert wordent). Bei Paarung seiner Bastarde erhielt Lang trotz jahrelanger… (More)