Tight Closure and plus Closure in Dimension Two
نویسنده
چکیده
We prove that the tight closure and the graded plus closure of a homogeneous ideal coincide for a two-dimensional N-graded domain of finite type over the algebraic closure of a finite field. This answers in this case a “tantalizing question” of Hochster. Mathematical Subject Classification (2000): 13A35; 14H60
منابع مشابه
Forcing Algebras, Syzygy Bundles, and Tight Closure
We give a survey about some recent work on tight closure and Hilbert-Kunz theory from the viewpoint of vector bundles. This work is based in understanding tight closure in terms of forcing algebras and the cohomological dimension of torsors of syzygy bundles. These geometric methods allowed to answer some fundamental questions of tight closure, in particular the equality between tight closure a...
متن کاملF-regularity relative to modules
In this paper we will generalize some of known results on the tight closure of an ideal to the tight closure of an ideal relative to a module .
متن کامل1 1 Ju l 2 00 3 The Theory of Tight Closure from the Viewpoint of Vector Bundles
Contents Introduction 3 1. Foundations 13 1.1. A survey about the theory of tight closure 13 1.2. Solid closure and forcing algebras 23 1.3. Cohomological dimension 25 1.4. Vector bundles, locally free sheaves and projective bundles 28 2. Geometric interpretation of tight closure via bundles 30 2.1. Relation bundles 30 2.2. Affine-linear bundles arising from forcing algebras 32 2.3. Cohomology ...
متن کاملTight Closure of Finite Length Modules in Graded Rings
In this article, we look at how the equivalence of tight closure and plus closure (or Frobenius closure) in the homogeneous m-coprimary case implies the same closure equivalence in the non-homogeneous m-coprimary case in standard graded rings. Although our result does not depend upon dimension, the primary application is based on results known in dimension 2 due to the recent work of H. Brenner...
متن کاملTight Closure and plus Closure for Cones over Elliptic Curves
We characterize the tight closure of graded primary ideals in a homogeneous coordinate ring over an elliptic curve by numerical conditions and we show that it is in positive characteristic the same as the plus closure.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005