Related papers: Analytic classification of plane branches up to mu…

In this paper, we use elementary method to give a classification of the multiplicative maps on matrix algebra $M_{n}(\mF)$ over a field $\mF$ of characteristic $0$. All the multiplicative maps are classified into three classes: the trivial…

We study cubic rational maps that take lines to plane curves. A complete description of such cubic rational maps concludes the classification of all planarizations, i.e., maps taking lines to plane curves.

We classify rank two vector bundles on a given del Pezzo threefold of degree four whose projectivizations are weak Fano into seven cases. We also give an example for each of these seven cases.

We consider smooth surfaces $S \subset \Pq$ containing a plane curve $P$ and prove some general result concerning the linear system $|H-P|$. We then look at regular surfaces lying on hypersurfaces of degree $s$ having a plane of…

We develop a cohomological method to classify amalgams of groups. We generalize this to simplicial amalgams in any concrete category. We compute the non-commutative 1-cohomology for several examples of amalgams defined over small simplices.

We construct small models of number fields and deduce a better bound for the number of number fields of given degree and bounded discriminant.

We study the algebraic Brauer classes on open del Pezzo surfaces of degree $4$. I.e., on the complements of geometrically irreducible hyperplane sections of del Pezzo surfaces of degree $4$. We show that the $2$-torsion part is generated by…

The Kuperberg Program asks to find presentations of planar algebras and use these presentations to prove results about their corresponding categories purely diagrammatically. This program has been completed for index less than 4 and is…

We study bipartite maps on the plane with one infinite face and one face of perimeter 2. At first we consider the problem of their enumeration an then study the connection between the combinatorial structure of a map and the degree of its…

We study minimally Terracini finite sets of points in the projective plane and we prove that the sequence of the cardinalities of minimally Terracini sets can have any number of gaps for degree great enough.

A finite, normal cover $f: X\longrightarrow \bbP^2$ of degree $m\geq 3$ (the case $m=2$ is well known and we do not consider it in this paper) is called \emph{simple}, if there is a pencil $\mathcal P$ of rational curves of $\bbP^2$ such…

We classify the gradings on the Kac superalgebra up to equivalence.

We compute the Picard groups with integral coefficients of the Hurwitz stacks parametrizing degree $4$ and $5$ covers of $\mathbb{P}^1$. As a consequence, we also determine the integral Picard groups of the Hurwitz stacks parametrizing…

We compute the limit shape for several classes of restricted integer partitions, where the restrictions are placed on the part sizes rather than the multiplicities. Our approach utilizes certain classes of bijections which map limit shapes…

In planar N=4 SYM we study a particular class of helicity preserving amplitudes. These are scalar amplitudes whose flavor configuration is chosen in such a way that only a limited number of diagrams is allowed, which exhibit an iterative…

In this paper we present the complete classification of caps in PG(4,2). These results have been obtained using a computer based exhaustive search that exploits projective equivalence.

We define, for an arbitrary partially ordered set, a multi-variable polynomial generalizing the hook polynomial.

We obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

We classify crossed product gradings for arbitrary groups and fields up to several equivalence relations in terms of group actions and their orbits.

This article is devoted to studying multiplicity and regularity of real analytic sets. We present an equivalence for real analytic sets, named blow-spherical equivalence, which generalizes differential equivalence and subanalytic…