arXiv subjects

Marc Chardin

Publications and source records attributed to Marc Chardin.

40 records · Page 3Linked to original sources

arXiv2002

Liaison and Castelnuovo-Mumford regularity

In this article we establish bounds for the Castelnuovo-Mumford regularity of projective schemes in terms of the degrees of their defining equations. The main new ingredient in our proof is to show that generic residual intersections of complete intersection rational singularities again have rational singularities. When applied to the theory of residual intersections this circle of ideas also sheds new light on some known classes of free resolutions of residual ideals.

math.AC↗

arXiv2002

Projective schemes: What is Computable in low degree?

This article first presents two examples of algorithms that extracts information on scheme out of its defining equations. We also give a review on the notion of Castelnuovo-Mumford regularity, its main properties (in particular its relation to computational issues) and different ways that were used to estimate it.

math.AC↗

arXiv2002

Castelnuovo-Mumford regularity: Examples of curves and surfaces

The behaviour of Castelnuovo-Mumford regularity under ``geometric'' transformations is not well understood. In this paper we are concerned with examples which will shed some light on certain questions concerning this behaviour.

math.AC↗

arXiv2002

Cohomology of projective schemes: From annihilators to vanishing

We provide bounds on the Castelnuovo-Mumford regularity in terms of ``defining equations'' by using elements that annihilates some cohomology modules, inspired by works of Miyazaki, Nagel, Schenzel and Vogel. The elements in these annihilators are provided either by liaison or by tight closure theories. Our results hold in any characteristic.

math.AC↗