A broken circuit ring.
A counterexample to a conjecture on linear systems on .
A note on the Hilbert scheme of curves of degree and genus .
A priori bounds of Castelnuovo type for cohomological Hilbert functions.
A restriction theorem and the Poincare series for U-invariants.
ACM sets of points in multiprojective space
Associated graded rings and connected sums
In 2012, Ananthnarayan, Avramov and Moore gave a new construction of Gorenstein rings from two Gorenstein local rings, called their connected sum. In this article, we investigate conditions on the associated graded ring of a Gorenstein Artin local ring , which force it to be a connected sum over its residue field. In particular, we recover some results regarding short, and stretched, Gorenstein Artin rings. Finally, using these decompositions, we obtain results about the rationality of the Poincaré...