Regularity and Resolutions for Multigraded Modules
نویسندگان
چکیده
This paper is concerned with the relationships between two concepts, vanishing of cohomology groups and the structure of free resolutions. In particular, we study the connection between vanishing theorems for the local cohomology of multigraded modules and the structure of their free multigraded resolutions.
منابع مشابه
- Invariant and the Minimal Free Resolution Huy
In recent years, two different multigraded variants of Castelnuovo-Mumford regularity have been developed, namely multigraded regularity, defined by the vanishing of multigraded pieces of local cohomology modules, and the resolution regularity vector, defined by the multi-degrees in a minimal free resolution. In this paper, we study the relationship between multigraded regularity and the resolu...
متن کاملMinimal Free Resolutions and Asymptotic Behavior of Multigraded Regularity
Let S be a standard N-graded polynomial ring over a field k, let I be a multigraded homogeneous ideal of S, and let M be a finitely generated Z-graded Smodule. We prove that the resolution regularity, a multigraded variant of CastelnuovoMumford regularity, of IM is asymptotically a linear function. This shows that the well known Z-graded phenomenon carries to the multigraded situation.
متن کاملMultigraded Castelnuovo-mumford Regularity
We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric geometry, we work with modules over a polynomial ring graded by a finitely generated abelian group. As in the standard graded case, our definition of multigraded regularity involves the vanishing of graded components of local cohomology. We establish the key properties of regularity: its connection with the m...
متن کاملFree Resolutions and Change of Rings
Projective resolutions of modules over a ring R are constructed starting from appropriate projective resolutions over a ring Q mapping to R. It is shown that such resolutions may be chosen to be minimal in codimension ≤ 2, but not in codimension 3. This is used to obtain minimal resolutions for essentially all modules over local (or graded) rings R with codimension ≤ 2. Explicit resolutions are...
متن کاملMultigraded Regularity: Syzygies and Fat Points Jessica Sidman and Adam Van Tuyl
The Castelnuovo-Mumford regularity of a graded ring is an important invariant in computational commutative algebra, and there is increasing interest in multigraded generalizations. We study connections between two recent definitions of multigraded regularity with a view towards a better understanding of the multigraded Hilbert function of fat point schemes in P n1 × · · · × P k . Introduction L...
متن کامل