REGULARITY AND RESOLUTIONS FOR MULTIGRADED MODULES
نویسندگان
چکیده
منابع مشابه
Regularity and Resolutions for Multigraded Modules
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.
متن کاملShifts in Resolutions of Multigraded Modules
Upper bounds are established on the shifts in a minimal resolution of a multigraded module. Similar bounds are given on the coefficients in the numerator of the BackelinLescot rational expression for multigraded Poincaré series. Let K be a field and S = K[x1, . . . , xn] the polynomial ring with its natural n-grading. When I is an ideal generated by monomials in the variables x1, . . . , xn, th...
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 Modules
Let R = k[x1, . . . , xn] be a polynomial ring over a field k. We present a characterization of multigraded R-modules in terms of the minors of their presentation matrix. We describe explicitly the second syzygies of any multigraded R-module.
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2007
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s021949880700248x