Let A A be a noetherian connected graded algebra. We introduce and study homological invariants that are weighted sums of the internal ...

We characterize all graphs whose binomial edge ideals have a linear resolution. Indeed, we show that complete graphs are the only graphs with this property. We also compute some graded components of the first Betti number of the binomial edge ideal of a graph with respect to the graphical terms. Finally, we give an upper bound for the Castelnuovo-Mumford regularity of the binomial edge ideal of...

This article comes from our quest for bounds on the Castelnuovo-Mumford regularity of schemes in terms of their “defining equations”, in the spirit of [BM], [BEL], [CP] or [CU]. The references [BS], [BM], [V] or [C] explains how this notion of regularity is a mesure of the algebraic complexity of the scheme, and provides several computational motivations. It was already remarked by several auth...

Bounds for the Castelnuovo-Mumford regularity and Hilbert coefficients are given in terms of the arithmetic degree (if the ring is reduced) or in terms of the defining degrees. From this it follows that there exists only a finite number of Hilbert functions associated to reduced algebras over an algebraically closed field with a given arithmetic degree and dimension. A good bound is also given ...

We investigate the asymptotic behaviour of Castelnuovo-Mumford regularity Ext and Tor, with respect to homological degree, over complete intersection rings. derive from a theorem Gulliksen linearity result for modules in high degrees. show similar under additional hypothesis that enough Tor are supported dimension at most one; we then provide examples showing could be pretty hectic when latter ...