Determinantal rings and varieties have been a central topic of commutative algebra and
algebraic geometry for several decades. Numerous researchers have contributed to the …

Page 1 DE GRUYTER Mauro C. Beltrametti, Andrew J. Sommese THE ADJUNCTION THEORY
OF COMPLEX PROJECTIVE VARIETIES DE GRUYTER EXPOSITIONS IN MATHEMATICS DE G …

This paper is a survey of computational issues in algebraic geometry, with particular
attention to the theory of Grobner bases and the regularity of an algebraic variety. 1. A …

In this paper the asymptotic behavior of the Castelnuovo $ ndash; Mumford regularity of
powers of a homogeneous ideal I is studied. It is shown that there is a linear bound for the …

Let I be an ideal in a polynomial ring over a perfect field. We given new methods for
computing the equidimensional parts and radical of I, for localizing I with respect to another …

Let $ S $ be a polynomial ring over a field. For a graded $ S $-module generated in degree
at most $ P $, the Castelnuovo-Mumford regularity of each of (i) its $ n^{\operatorname {th}} …

In recent years, the equations defining a projective variety X= P'and the syzygies among
them have attracted considerable attention. Classical results giving conditions to guarantee …

We introduce the notion of Mukai regularity ($ M $-regularity) for coherent sheaves on
abelian varieties. The definition is based on the Fourier-Mukai transform, and in a special …

Our main theorem shows that the regularity of nondegenerate homogeneous prime ideals is
not bounded by any polynomial function of the degree; this holds over any field $ k $. In …

Providing an introduction to both classical and modern techniques in projective algebraic
geometry, this monograph treats the geometrical properties of varieties embedded in …