Related papers: ${\mathbb P}^1$-gluing for local complete intersec…

In this article we investigate when a complete ideal in a two-dimensional regular local ring is a multiplier ideal of some ideal with an integral multiplying parameter. In particular, we show that this question is closely connected to the…

Let $R$ be a commutative Noetherian ring of prime characteristic $p$. In this paper we give a short proof using filter regular sequences that the set of associated prime ideals of $H^t_I(R)$ is finite for any ideal $I$ and for any $t \ge 0$…

We study three classes of local homomorphisms and their behavior with respect to the ascent and descent of the \emph{complete intersection} property. Crucially, they fall in between the already studied classes of complete intersection and…

The tilting correspondence is a fundamental property of perfectoid fields. In this note, we show that the tilting construction can also be used to detect perfectoid fields among nonarchimedean fields. In particular, for $K$ a complete…

Let $K$ be a field and let $R = K[X_1, \ldots, X_m]$ with $m \geq 2$. Give $R$ the standard grading. Let $I$ be a homogeneous ideal of height $g$. Assume $1 \leq g \leq m -1$. Suppose $H^i_I(R) \neq 0$ for some $i \geq 0$. We show (1)…

Let $A$ denote an affine algebra over an algebraically closed field $k$, with $\dim A=d\geq 3$. In the light of availability of cancellation theorems for stably free modules $P$ with $rank(P)=d-1$ (corank one), we try to implement the…

We show that each local field $\mathbb{F}_q((t))$ of characteristic $p > 0$ is characterised up to isomorphism within the class of all fields of imperfect exponent at most $1$ by (certain small quotients of) its absolute Galois group…

We characterize the graphs $G$ for which their toric ideals $I_G$ are complete intersections. In particular we prove that for a connected graph $G$ such that $I_G$ is complete intersection all of its blocks are bipartite except of at most…

For a Noetherian commutative ring $R$, let $H^i_I(R)$ be the $ i$-th local cohomology module of $R$ with respect to $I$. In \cite{Hel-08}, Hellus posed the question of identifying rings $R$ such that $\operatorname{injdim}_R…

Let $L_n$ be a line graph with $n$ edges and $\F(L_n)$ the facet ideal of its matching complex. In this paper, we provide the irreducible decomposition of $\F(L_n)$ and some exact formulas for the projective dimension and the regularity of…

We define the covering gonality and separable covering gonality of varieties over arbitrary fields, generalizing the definition given by Bastianelli-de Poi-Ein-Lazarsfeld-Ullery for complex varieties. We show that over an arbitrary field a…

In this paper we prove an explicit, computable upper bound on the Hartshorne-Speiser-Lyubeznik number of the local cohomology of a pointed, affine semigroup ring over a perfect field of positive characteristic. This bound depends only on…

Let $(Q,\mathfrak{n})$ be a regular local ring of dimension $c \geq 2$ with algebraically closed residue field $k = Q/\mathfrak{n}$. Let $f_1, f_2, \ldots f_{c-1}, g$ be a regular sequence in $Q$ such that $ f_i \in \mathfrak{n}^2$ for all…

We consider a junction between surface $p$-type and surface $n$-type on an ideal topological insulator in which carrier type and density in two adjacent regions are locally controlled by composition graded doping or electrical gating. Such…

We prove an "abelian, locally compact" Whitehead theorem in fine shape: A fine shape morphism between locally connected finite-dimensional locally compact separable metrizable spaces with trivial $\pi_0$ and $\pi_1$ is a fine shape…

Suppose $k\nmid n$ and $H$ is an $n$-vertex $k$-uniform hypergraph. A near perfect matching in $H$ is a matching of size $\lfloor n/k\rfloor$. We give a divisibility barrier construction that prevents the existence of near perfect matchings…

This is essentially an erratum, with some example to indicate inconsistencies. Suppose $A=k[X_1, X_2, \ldots, X_n]$ is a polynomial ring over a field $k$. The Complete Intersection conjecture states that, for any ideal $I$ in $A$,…

We provide a novel proof of the homological excess intersection formula for local complete intersections. The novelty is that the proof makes use of global morphisms comparing the intersections to a self intersection.

We introduce an infinite variant of hypersurface support for finite-dimensional, noncommutative complete intersections. By a noncommutative complete intersection we mean an algebra R which admits a smooth deformation $Q\to R$ by a…

Over an arbitrary field $\mathbb{F}$, Harbourne conjectured that $$I^{(N (r-1)+1)} \subseteq I^r$$ for all $r>0$ and all homogeneous ideals $I$ in $S = \mathbb{F} [\mathbb{P}^N] = \mathbb{F} [x_0, \ldots, x_N]$. The conjecture has been…