相关论文: Computing the tight closure in dimension two
We show that the Hilbert-Kunz multiplicity is a rational number for an R_+-primary homogeneous ideal I=(f_1, ..., f_n) in a two-dimensional graded domain R of finite type over an algebraically closed field of positive characteristic.…
In this work, we consider the problem of computing triangular bases of integral closures of one-dimensional local rings. Let $(K, v)$ be a discrete valued field with valuation ring $\mathcal{O}$ and let $\mathfrak{m}$ be the maximal ideal.…
This paper establishes the fundamental properties of the $s$-closures, a recently introduced family of closure operations on ideals of rings of positive characteristic. The behavior of the $s$-closure of homogeneous ideals in graded rings…
Let $R$ be an excellent Noetherian ring of prime characteristic. Consider an arbitrary nested pair of ideals (or more generally, a nested pair of submodules of a fixed finite module). We do \emph{not} assume that their quotient has finite…
We consider the computation of syzygies of multivariate polynomials in a finite-dimensional setting: for a $\mathbb{K}[X_1,\dots,X_r]$-module $\mathcal{M}$ of finite dimension $D$ as a $\mathbb{K}$-vector space, and given elements…
In this paper we exhibit an example of a three-dimensional regular local domain (A, n) having a height-two prime ideal P with the property that the extension PA^ of P to the n-adic completion A^ of A is not integrally closed. We use a…
We compute the Harder-Narasimhan filtration of vector bundles $f_*\mathcal O_Y$ for certain finite morphisms $f\,:\,Y\,\longrightarrow\, X$ and in some other cases.
The Qth-power algorithm for computing structured global presentations of integral closures of affine domains over finite fields is modified to compute structured presentations of integral closures of ideals in affine domains over finite…
An ideal of a local polynomial ring can be described by calculating a standard basis with respect to a local monomial ordering. However standard basis algorithms are not numerically stable. Instead we can describe the ideal numerically by…
Herzog and Srinivasan have conjectured that for any homogeneous k-algebra, the degree is bounded above by a function of the maximal degrees of the syzygies. Combining the syzygy quadrangle decomposition of Peeva and Sturmfels and a delicate…
We provide a negative answer to an old question in tight closure theory by showing that the containment x^3y^3 \in (x^4,y^4,z^4)^* in K[x,y,z]/(x^7+y^7-z^7) holds for infinitely many but not for almost all prime characteristics of the field…
In recent years, multiplier ideals have found many applications in local and global algebraic geometry. Because of their importance, there has been some interest in the question of which ideals on a smooth complex variety can be realized as…
We present an algorithm for computing the integral closure of a reduced ring that is finitely generated over a finite field.
Using the fact that the structure sheaf of a resolution of singularities, or regular alteration, pushes forward to a Cohen-Macaulay complex in equal characteristic zero with a differential graded algebra structure, we introduce a…
An analogue of the theory of integral closure and reductions is developed for a more general class of closures, called Nakayama closures. It is shown that tight closure is a Nakayama closure by proving a ``Nakayama lemma for tight…
In this article we give an algorithm for computing the integral closure of a reduced Noetherian ring R, in case this integral closure is finitely generated over R.
It is shown that tight closure commutes with localization in any two dimensional ring $R$ of prime characteristic if either $R$ is a Nagata ring or $R$ possesses a weak test element. Moreover, it is proved that tight closure commutes with…
We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results are obtained by…
Let $\Omega$ be a bounded domain of $\mathbb{R}^3$ whose closure $\overline{\Omega}$ is polyhedral, and let $\mathcal{T}$ be a triangulation of $\overline{\Omega}$. Assuming that the boundary of $\Omega$ is sufficiently regular, we provide…
Tight closure test ideals have been central to the classification of singularities in rings of characteristic $p>0$, and via reduction to characteristic $p$, in equal characteristic zero as well. A summary of their properties and…