Related papers: The impossibility of extending the Naimark complem…

We give a bound on the minimal number of singularities of a nodal projective complete intersection threefold which contains a smooth complete intersection surface that is not a Cartier divisor.

In this short note, we prove the claim of the title.

It is shown that modified gravity theories with a Lagrangian composed of the three quadratic invariants of the Riemann curvature tensor are not appropriate. The field equations are either incompatible and/or irregular [like f(R)-gravities],…

This paper is devoted to the study of non-existence of certain type of convex functions on a Riemannian manifold with a pole. To this end, we have developed the notion of odd and even function on a Riemannian manifold with a pole and proved…

The notion of essential submodules and essential extensions of modules are extended to groups (typically nonabelian), and several necessary and sufficient conditions for a group to possess a proper essential subgroup are investigated.…

We give a simple proof of why there is a Matrix theory approximation for a membrane shaped like an arbitrary Riemann surface. As corollaries, we show that noncompact membranes cannot be approximated by matrices and that the Poisson algebra…

We prove the boundedness of $n$-complements for surface pairs in a generalized case without restrictions on multiplicities or the Fano type assumption.

We give topological characterizations of filters $F$ on $w$ such that the Mathias forcing $M_F$ adds no dominating reals or preserves ground model unbounded families. This allows us to answer some questions of Brendle, Guzm\'an,…

In this short note we reduce the b-semiampleness conjecture for lc-trivial fibrations to the b-semiampleness conjecture for klt-trivial fibrations.

We show that no exotic $\mathbb{R}^4$ admits a complete Riemannian metric with uniformly positive isotropic curvature and with bounded geometry. This is essentially a corollary of the main result in [Hu1], and was stated in [Hu2] without…

We investigate finite field extensions of the unital 3-field, consisting of the unit element alone, and find considerable differences to classical field theory. Furthermore, the structure of their automorphism groups is clarified and the…

In this paper we prove that no consistent finitely axiomatized theory one-dimensionally interprets its own extension with predicative comprehension. This constitutes a result with the flavor of the Second Incompleteness Theorem whose…

We exhibit a 3-manifold which admits no tight contact structure.

We give examples of non-fibered hyperbolic knot complements in homology spheres that are not commensurable to fibered knot complements in homology spheres. In fact, we give many examples of knot complements in homology spheres with the…

In this paper we study the existence of gradings on finite dimensional associative algebras. We prove that a connected algebra $A$ does not have a non-trivial grading if and only if $A$ is basic, its quiver has one vertex, and its group of…

Conformal fundamental forms populate a minimal generating set for low differential order invariants of conformal hypersurface embeddings. In this work we complete the characterization of conformal fundamental forms by proving the general…

The main result of the present paper, combined with earlier results of Hardt and Lin settles the extension problem for $W^{1,p}(\mathcal M, \mathcal N)$, where $\mathcal M$ and $\mathcal N$ are compact riemannian manfolds, $\mathcal M$…

We present a novel parabolic reflector system capable of generating a broader class of shapes beyond canonical parabolas. Using a discretized framework, we construct meshes corresponding to key families of developable surfaces, including…

Let F be a set of relational trees and let Forbh(F) be the class of all structures that admit no homomorphism from any tree in F; all this happens over a fixed finite relational signature $\sigma$. There is a natural way to expand Forbh(F)…

The existence of a nowhere zero real vector field implies a well-known restriction on a compact manifold. But all manifolds admit nowhere zero complex vector fields. The relation between these observations is clarified.