Related papers: Torsion orders of complete intersections
A group element is called a generalized torsion if a finite product of its conjugates is equal to the identity. We prove that in a nilpotent or FC-group, the generalized torsion elements are all torsion elements. Moreover, we compute the…
We provide a structure theorem for all almost complete intersection ideals of depth three in any Noetherian local ring. In particular, we find that the minimal generators are the pfaffians of suitable submatrices of an alternating matrix.…
We study the question of the existence of a decomposition of the diagonal for very general quartic and $(2,3)$-complete intersection $n$-folds. Using cycle-theoretic techniques of Lange, Pavic and Schreieder we reduce the question via a…
This paper shows that for the domain intersection $\dom T\cap\dom T^*$ of a closed linear operator and its Hilbert space adjoint everything is possible for very common classes of operators with non-empty resolvent set. Apart from the most…
Since the works of Krasnov and Scheiderer, there has been an interest in studying effective totally real divisors on a curve X defined over a real closed field, i.e., effective divisors supported on the real locus. Scheiderer proved that,…
Let $X \subset \mathbb{P}^n$ be a general Fano complete intersection of type $(d_1,\dots, d_k)$. If at least one $d_i$ is greater than $2$, we show that $X$ contains rational curves of degree $e \leq n$ with balanced normal bundle. If all…
The descent method is one of the approaches to study the Brauer--Manin obstruction to the local--global principle and to weak approximation on varieties over number fields, by reducing the problem to ``descent varieties''. In recent lecture…
Oriented loops on an orientable surface are, up to equivalence by free homotopy, in one-to-one correspondence with the conjugacy classes of the surface's fundamental group. These conjugacy classes can be expressed (not uniquely in the case…
We complete the proof of the Nisnevich conjecture in equal characteristic: for a smooth algebraic variety $X$ over a field $k$, a $k$-smooth divisor $D \subset X$, and a reductive $X$-group $G$ whose base change $G_D$ is totally isotropic,…
We investigate decompositions of Betti diagrams over a polynomial ring within the framework of Boij--Soederberg theory. That is, given a Betti diagram, we decompose it into pure diagrams. Relaxing the requirement that the degree sequences…
A forcing set for a perfect matching of a graph is defined as a subset of the edges of that perfect matching such that there exists a unique perfect matching containing it. A complete forcing set for a graph is a subset of its edges, such…
The classification of elliptic curves E over the rationals Q is studied according to their torsion subgroups E_{tors}(Q) of rational points. Explicit criteria for the classification are given when E_{tors}(Q) are cyclic groups with even…
It is proved in this paper that a locally complete intersection curve in a smooth affine C-algebra with trival conormal bundle is a set theoretic complete intersection if its corresponding class in the Grothendieck Group is torsion.
Given an ordered sequence of $N$-choose-2 integers, we give necessary and sufficient conditions to have an ordered collection of $N$ simple closed curves on a torus such that the algebraic pairwise intersections of those curves are the…
A restricted $d$th power of an ideal $I$ is obtained by restricting the exponent vectors allowed to appear on the "natural" generating set of $I^d$, for some integer $d$. In this paper, we study homological properties of restricted powers…
For any simple digraph $D$ we offer a new proof for the intersection number of its middle digraph, $M(D)$; while doing so we also solve for the intersection number when $D$ has loops. In addition, a new transformation, the union of $D$ and…
We obtain new lower and upper bounds for the maximum multiplicity of some weighted and, respectively, non-weighted common geometric graphs drawn on n points in the plane in general position (with no three points collinear): perfect…
We extend the descent theory of Colliot-Th\'el\`ene and Sansuc to arbitrary smooth algebraic varieties by removing the condition that every invertible regular function is constant. This links the Brauer--Manin obstruction for integral…
A poset $\bfp$ is well-partially ordered (WPO) if all its linear extensions are well orders~; the supremum of ordered types of these linear extensions is the {\em length}, $\ell(\bfp)$ of $\bfp$. We prove that if the vertex set $X$ of…
In recent work of T. Cassidy and the author, a notion of complete intersection was defined for (non-commutative) regular skew polynomial rings, defining it using both algebraic and geometric tools, where the commutative definition is a…