3 research outputs found
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
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.Comment: 19 pages. To appear in "American Journal of Mathematics
Matrix representations for toric parametrizations
In this paper we show that a surface in P^3 parametrized over a 2-dimensional
toric variety T can be represented by a matrix of linear syzygies if the base
points are finite in number and form locally a complete intersection. This
constitutes a direct generalization of the corresponding result over P^2
established in [BJ03] and [BC05]. Exploiting the sparse structure of the
parametrization, we obtain significantly smaller matrices than in the
homogeneous case and the method becomes applicable to parametrizations for
which it previously failed. We also treat the important case T = P^1 x P^1 in
detail and give numerous examples.Comment: 20 page