Related papers: On the splitting of the Kummer exact sequence
We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
We classify absolutely split vector bundles on proper $k$-schemes. More precise, we prove that the closed points of the Picard scheme are in one-to-one correspondence with indecomposable absolutely split vector bundles. Furthermore, we…
In this note, we present a probabilistic proof of the well-known finite geometric series. The proof follows by taking the moments of the sum and the difference of two independent exponentially distributed random variables.
We give a method for constructing Kummer covers with many points over finite fields.
In this paper we prove an identity in terms of generating functions which enables us to calculate the numbers of isomorphism classes of absolutely indecomposable semistable representations of quivers over finite fields.
We investigate a result on convergence of double sequences of numbers and how it extends to measurable functions.
Some curvature properties of Kahler manifolds of indefinite metrics are studied. Analogues of a Kulkarni's theorem are proved for such manifolds.
We explicitly construct the Kummer variety associated to the Jacobian of a hyperelliptic curve of genus 3 that is defined over a field of characteristic not equal to 2 and has a Weierstra{\ss} point defined over the same field. We also…
We obtain a new important basic result on splice-quotient singularities in an elegant combinatorial-geometric way: every level of the divisorial filtration of the ring of functions is generated by monomials of the defining coordinate…
We pose the problem to determine explicit defining equations of various elliptic fibrations on a given $K3$ surface, and study the case of the Kummer surfaces of the product of two elliptic curves.
We compute the Weierstrass semigroup at one totally ramified place for Kummer extensions defined by $y^m=f(x)^{\lambda}$ where $f(x)$ is a separable polynomial over $\mathbb{F}_q$. In addition, we compute the Weierstrass semigroup at two…
We present an overview of the notions of exact sequences of Hopf algebras and tensor categories and their connections. We also present some examples illustrating their main features; these include simple fusion categories and a natural…
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
Several structural properties of a universal algebra can be seen from the higher commutators of its congruences. Even on a finite algebra, the sequence of higher commutator operations is an infinite object. In the present paper, we exhibit…
We provide a polynomial time cutting plane algorithm based on split cuts to solve integer programs in the plane. We also prove that the split closure of a polyhedron in the plane has polynomial size.
Using a special metric in the space of sequences, we give a geometric description of almost periodic sets in the $k$-dimensional Euclidean space. We prove the completeness of the space of almost periodic sets and some analogue of the…
This paper is concerned with the problem of determining the number of division algebras which share the same collection of finite splitting fields. As a corollary we are able to determine when two central division algebras may be…
We establish a connection between the coefficients of Artin-Mazur zeta-functions and Kummer congruences. This allows to settle positively the question of the existence of a map T such that the number of fixed points of the n-th iterate of T…
In this paper we consider elliptic divisibility sequences generated by a point on an elliptic curve over $\mathbb{Q}$ with $j$-invariant $1728$ given by an integral short Weierstrass equation. For several different such elliptic…
In the paper we describe the almost split sequences in the homotopy category of perfect complexes over a gentle algebra.