Related papers: Hungarian Cubes
Effective bounds for the finite number of surjective holomorphic maps between canonically polarized compact complex manifolds of any dimension with fixed domain are proven. Both the case of a fixed target and the case of varying targets are…
We show that there are infinitely many triples of positive integers a, b, c (greater than 1) such that ab + 1, ac + 1, bc + 1 and abc + 1 are all perfect squares.
We give a complete description of the arboreal Galois representation of a certain postcritically finite cubic polynomial over a large class of number fields and for a large class of basepoints. This is the first such example that is not…
An identity is proved connecting two finite sums of inverse tangents. This identity is discretized version of Jacobi's imaginary transformation for the modular angle from the theory of elliptic functions. Some other related identities are…
We show that $X^\lambda$ is strongly homogeneous whenever $X$ is a non-separable zero-dimensional metrizable space and $\lambda$ is an infinite cardinal. This partially answers a question of Terada, and improves a previous result of the…
We define and study entanglement of continuous positive definite functions on products of compact groups. We formulate and prove an infinite-dimensional analog of Horodecki Theorem, giving a necessary and sufficient criterion for…
We prove that if there is an elementary embedding from the universe to itself, then there is a proper class of measurable successor cardinals.
A proof that the set of real numbers is denumerable is given.
We give a new proof of the finiteness of B-representations. As a consequence of the finiteness of B-representations and Koll\'ar's gluing theory on lc centers, we prove that the (relative) abundance conjecture for slc pairs is implied by…
Answering a question of Usuba, we show that an extendible cardinal can be preserved by a set forcing that is not a small forcing.
The existence of a positive solution to a class of Choquard equations with potential going at a positive limit at infinity possibly from above or oscillating is proved. Our results include the physical case and do not require any symmetry…
We show that for any Polish group $G$ and any countable normal subgroup $\Gamma\triangleleft G$, the coset equivalence relation $G/\Gamma$ is a hyperfinite Borel equivalence relation. In particular, the outer automorphism group of any…
For a cardinal $\mathfrak{a}$, let $\mathrm{fin}(\mathfrak{a})$ be the cardinality of the set of all finite subsets of a set which is of cardinality $\mathfrak{a}$. It is proved without the aid of the axiom of choice that for all infinite…
We give an explicit necessary condition for pairs of orders in a quartic CM-field to have the same polarised class group. This generalises a simpler result for imaginary quadratic fields. We give an application of our results to computing…
We show that the number of deformation types of canonically polarized manifolds over an arbitrary variety with proper singular locus is finite, and that this number is uniformly bounded in any finite type family of base varieties. As a…
We analyze a natural function definable from a scale at a singular cardinal, and using this function we are able to obtain quite strong negative square-brackets partition relations at successors of singular cardinals. The proof of our main…
We introduce an infinite set of integer mappings that generalize the well-known Collatz-Ulam mapping and we conjecture that an infinite subset of these mappings feature the remarkable property of the Collatz conjecture, namely that they…
In this paper we solve the polarization problem for real Hilbert spaces, a long-standing conjecture that had remained open for nearly three decades. We also confirm that the only extremal configurations are orthonormal sets. These are…
It is proved that the non-rationality of a generic cubic fourfold follows from a conjecture on the non-decomposability in the direct sum of non-trivial polarized Hodge structures of the polarized Hodge structure on transcendental cycles on…
We obtain an exact formula for the cubic partition function and prove a conjecture by Banerjee, Paule, Radu and Zeng.