Related papers: Acyclic complexes and 1-affineness
We present a variant of the Peskine--Szpiro Acyclicity Lemma, and hence a way to certify exactness of a complex of finite modules over a large class of (possibly) noncommutative rings. Specifically, over the class of Auslander regular…
This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying…
A singular foliation $\mathcal F$ gives a partition of a manifold $M$ into leaves whose dimension may vary. Associated to a singular foliation are two complexes, that of the diffeological differential forms on the leaf space $M / \mathcal…
Using the random complexes of Linial and Meshulam, we exhibit a large family of simplicial complexes for which, whenever affinely embedded into Euclidean space, the filling areas of simplicial cycles is greatly distorted. This phenomenon…
This is an announcement of some of the results obtained as a part of the second author's Ph.D. thesis. In the first part, we prove that the fundamental group of an acylindrical complex of hyperbolic groups with finite edge groups is…
The affinely regular polygons in certain planar sets are characterized. It is also shown that the obtained results apply to cyclotomic model sets and, additionally, have consequences in the discrete tomography of these sets.
In this note we investigate to what extent the fundamental group of a metric space can be described as the inverse limit of its discrete fundamental groups. We show that some mild conditions suffice to imply the existence of an isomorphism…
Recently, it has been proved that if we have a field extension, then it has linear matching property if and only if L is purely transcendental or is an extension of prime degree. In this note we provide a counterexample for this result.
The purpose of this note is to provide exposition for a proof of the statement in the title. This idea, that arbitrary cohomology classes (of high enough degree) of a finite group $G$ can be trivialized in a finite group extension, has been…
We modify Grayson's model of $K_1$ of an exact category to give a presentation whose generators are binary acyclic complexes of length at most $k$ for any given $k \ge 2$. As a corollary, we obtain another, very short proof of the…
We will review the main results concerning the automorphism groups of saturated structures which were obtained during the two last decades. The main themes are: the small index property in the countable and uncountable cases; the…
A long standing problem in the area of error correcting codes asks whether there exist good cyclic codes. Most of the known results point in the direction of a negative answer. The uncertainty principle is a classical result of harmonic…
In this paper we prove a new characterization of the distinguished unipotent orbits of a connected reductive group over an algebraically closed field of characteristic 0. For classical groups we prove the characterization by a combinatorial…
We show that if an open cover of a finite dimensional space is equivariant with respect to some finite group action on the space then there is an equivariant refinement of bounded dimension. This will generalize some constructions of…
This note points out a gap in the proof of one of the technical results in the paper "Asymptotic Invariants of Base Loci", that appeared in Ann. Inst. Fourier (Grenoble) 56 (2006), 1701-1734. We provide a correct proof of this result.
Let M be a rank 1 affine invariant orbifold in a stratum of the moduli space of flat surfaces. We show that the leaves of the M-isoperiodic foliation are either all closed or all dense. In the second case, we establish ergodicity of the…
This small text was written for the AMS Notices. It is a survey of integrality properties of complex local systems, where I tried to single out one example which is not entirely explicit in the literature. The focus is on the obstruction it…
We give an explicit description of the irreducible components of the moduli spaces of polarized Enriques surfaces in terms of decompositions of the polarization as an effective sum of isotropic classes. We prove that infinitely many of…
Toral automorphisms, represented by unimodular integer matrices, are investigated with respect to their symmetries and reversing symmetries. We characterize the symmetry groups of GL(n,Z) matrices with simple spectrum through their…
Contents 1. Algebraicity criterion: statement 2. Proof of the algebraicity criterion. 3. Pseudoeffectivity and movable classes. 4. Harder-Narasimhan filtrations and pseudo-effectivity. 5. Pseudo-effectivity of relative canonical bundles. 6.…