Related papers: Monodromy and algebraic cycles
We introduce a geometric construction which relates to the pentagram map much in the way that a logarithmic spiral relates to a circle. After introducing the construction, we establish some basic geometric facts about it, and speculate on…
We study vanishing cycles naturally attached to a meromorphic function with isolated singularities, in both local and global settings.
Let $A$ be an integer matrix, and let $f_A$ be the associated monomial map. We give a connection between the eigenvalues of $A$ and existence of a linear recurrence relation in the sequence of degrees.
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
We show that the monodromy operator at infinity plus the decomposition of the homology given by the vanishing cycles completely determine the homology monodromy representation of any complex polynomial.
We introduce the notion of ends for algebras. The definition is analogous to the one in geometric group theory. We establish some relations to growth conditions and cyclic cohomology.
We investigate the notion of associated graded coalgebra (algebra) of a bialgebra with respect to a subbialgebra (quotient bialgebra) and characterize those which are bialgebras of type one in the framework of abelian braided monoidal…
The middle homology of the Milnor fiber of a quasihomogeneous polynomial with an isolated singularity is a ${\mathbb Z}$-lattice and comes equipped with an automorphism of finite order, the integral monodromy. Orlik (1972) made a precise…
Leibniz algebras generated by one element, called cyclic, provide simple and illuminating examples of many basic concepts. It is the purpose of this paper to illustrate this fact.
We investigate linearity of amalgams of subgroups of algebraic groups along intersections with algebraic subgroups. In the process, we establish linearity of certain "doubles" of linear groups, and obtain new examples of finitely generated…
In this note we prove that the constant and equivariant cyclic cohomology of algebras coincide. This shows that constant cyclic cohomology is rich and computable.
In the paper we show that for a normal-crossings degeneration $Z$ over the ring of integers of a local field with $X$ as generic fibre, the local monodromy operator and its powers determine invariant cocycle classes under the decomposition…
This is an expository article on the theory of algebraic stacks. After introducing the general theory, we concentrate in the example of the moduli stack of vector budles, giving a detailed comparison with the moduli scheme obtained via…
An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over an arbitrary finite field. For systems that can be…
We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras
In this paper, we study the notion of chordality and cycles in hypergraphs from a commutative algebraic point of view. The corresponding concept of chordality in commutative algebra is having a linear resolution. However, there is no…
In this paper, we shall give a candidate for the t-structure on the triangulated category of mixed motives due to Voevodsky.
q-rook monoid algebras, Hecke algebras and Schur-Weyl duality
The aim of the paper is to discuss the relations between the three kinds of objects named in the title. In a sense, this is a survey of such relations; however, some new directions are also considered. This relates, especially, to sections…
This is a list of some problems and conjectures related to various types of algebras, that is to algebraic operads. Some comments and hints are included.