Related papers: Measuring birational derived splinters
To study singularities on complex varieties we study Poincar\'e series of filtrations that are defined by discrete valuations on the local ring at the singularity. In all previous papers on this topic one poses restrictions on the centers…
We study the local symplectic algebra of the 1-dimensional isolated complete intersection singularity of type S{\mu}. We use the method of algebraic restrictions to classify symplectic S{\mu} singularities. We distinguish these symplectic…
The research field of spatial scientometrics is dedicated to measuring and analyzing science with spatial components (e.g., location, place, mapping). Because of the dynamic nature of this field, researchers from multidisciplinary domains…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent conditions. We show that global fields belong to this class, and…
This paper is motivated from a fundamental curiosity on what defines a category of object shapes. For example, we may have the common knowledge that a plane has wings, and a chair has legs. Given the large shape variations among different…
In this note, we investigate a mixture of combinatorial spectra and stratified simplicial sets, which would be thought of as a model of the spectrum objects of $(\infty, \infty)$-categories.
There is a construction which lies at the heart of descent theory. The combinatorial aspects of this paper concern the description of the construction in all dimensions. The description is achieved precisely for strict n-categories and…
In this paper we study derived categories of nodal singularities. We show that for all nodal singularities there is a categorical resolution whose kernel is generated by a $2$ or $3$-spherical object, depending on the dimension. We apply…
This paper is devoted to give all the technical constructions and definitions that will lead to the construction of an algorithm of resolution of singularities for binomial ideals. We construct a resolution function that will provide a…
We introduce a notion of discrete topological complexity in the setting of simplicial complexes, using only the combinatorial structure of the complex by means of the concept of contiguous simplicial maps. We study the links of this new…
A new criterion is developed which provides a check as to whether a chosen set of polarization observables is complete with respect to the determination of all independent $T$-matrix elements of a reaction of the type $a+b\to c+d+...$. As…
We construct small models of number fields and deduce a better bound for the number of number fields of given degree and bounded discriminant.
The discrete logarithm problem is a fundamental challenge in number theory with significant implications for cryptographic protocols. In this paper, we investigate the limitations of gradient-based methods for learning the parity bit of the…
An algebraizable singularity is a germ of a singular holomorphic foliation which can be defined in some appropriate local chart by a differential equation with algebraic coefficients. We show that there exists at least countably many…
We introduce a general framework allowing to apply the theory of regularity structures to discretisations of stochastic PDEs. The approach pursued in this article is that we do not focus on any one specific discretisation procedure.…
In this paper, we introduce poly-Bernoulli numbers with level $2$, related to the Stirling numbers of the second kind with level $2$, and study several properties of poly-Bernoulli numbers with level $2$ from their expressions, relations,…
We classify the singularities of a surface ruled by conics: they are rational double points of type $A_n$ or $D_n$. This is proved by showing that they arise from a precise series of blow-ups of a suitable surface geometrically ruled by…
A model of computation for which reasonable yet still incomplete lower bounds are known is the read-once branching program. Here variants of complexity measures successful in the study of read-once branching programs are defined and…
In this paper, we use (bi)semicosimplicial language to study the classical problem of infinitesimal deformations of a closed subscheme in a fixed smooth variety, defined over an algebraically closed field of characteristic 0. In particular,…