Cohomological dimension of ideals defining Veronese subrings
نویسندگان
چکیده
Given a standard graded polynomial ring over commutative Noetherian $A$, we prove that the cohomological dimension and height of ideals defining any its Veronese subrings are equal. This result is due to Ogus when $A$ field characteristic zero, follows from Peskine Szpiro positive characteristic; our applies, for example, integers.
منابع مشابه
Toric Ideals for High Veronese Subrings of Toric Algebras
We prove that the defining ideal of a sufficiently high Veronese subring of a toric algebra admits a quadratic Gröbner basis consisting of binomials. More generally, we prove that the defining ideal of a sufficiently high Veronese subring of a standard graded ring admits a quadratic Gröbner basis. This was proved by Eisenbud–Reeves–Totaro in the case where coordinates are generic. Our proof doe...
متن کاملInitial ideals, Veronese subrings, and rates of algebras
Let S be a polynomial ring over an infinite field and let I be a homogeneous ideal of S. Let Td be a polynomial ring whose variables correspond to the monomials of degree d in S. We study the initial ideals of the ideals Vd(I) ⊂ Td that define the Veronese subrings of S/I. In suitable orders, they are easily deduced from the initial ideal of I. We show that in(Vd(I)) is generated in degree ≤ ma...
متن کاملCohomological Dimension, Connectedness Properties and Initial Ideals
In this paper we will compare the connectivity dimension c(P/I) of an ideal I in a polynomial ring P with that of any initial ideal of I. Generalizing a theorem of Kalkbrener and Sturmfels [18], we prove that c(P/LT≺(I)) ≥ min{c(P/I), dim(P/I)−1} for each monomial order ≺. As a corollary we have that every initial complex of a Cohen-Macaulay ideal is strongly connected. Our approach is based on...
متن کاملOn Defining Ideals or Subrings of Hall Algebras
Let A be a finitary algebra over a finite field k, and A-mod the category of finite dimensional left A-modules. Let H(A) be the corresponding Hall algebra, and for a positive integer r let Dr(A) be the subspace of H(A) which has a basis consisting of isomorphism classes of modules in A-mod with at least r+1 indecomposable direct summands. If A is hereditary of type An, then Dr(A) is known to be...
متن کاملIdeals Contained in Subrings
Lewin has proved that if S is a ring and R a subring of finite index in S, then R contains an ideal of S which is also of finite index; and Feigelstock has recently shown that other classes of subrings must contain ideals belonging to the same class. We provide some extensions of these results, and apply them to prime rings. In the final section, we investigate finiteness of rings having only f...
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: Proceedings of the American Mathematical Society
سال: 2021
ISSN: ['2330-1511']
DOI: https://doi.org/10.1090/proc/15273