Related papers: Some elementary remarks on lci algebraic cycles
We prove the strong Lefschetz property for certain complete intersections defined by products of linear forms, using a characterization of the strong Lefschetz property in terms of central simple modules.
This chapter presents a state-of-the-art survey of relationships, traditionally referred to as `bridges', between interpolation properties for propositional logics -- including superintuitionistic, modal, and substructural logics -- and…
Recent developments in the categorical foundations of universal algebra have given fresh impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott's…
We introduce a new diagrammatic notation for representing the result of (algebraic) effectful computations. Our notation explicitly separates the effects produced during a computation from the possible values returned, this way simplifying…
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.
We characterize the graphs $G$ for which their toric ideals $I_G$ are complete intersections. In particular we prove that for a connected graph $G$ such that $I_G$ is complete intersection all of its blocks are bipartite except of at most…
This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.
Algebraic lattices are those obtained from modules in the ring of integers of algebraic number fields through the canonical or twisted embeddings. In turn, well-rounded lattices are those with maximal cardinality of linearly independent…
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
In recent work of T. Cassidy and the author, a notion of complete intersection was defined for (non-commutative) regular skew polynomial rings, defining it using both algebraic and geometric tools, where the commutative definition is a…
Here we briefly describe some topics along the lines of projective spaces and related geometric constructions connected to linear algebra, which provide fundamental examples in classical geometry and analysis.
Several generalizations of a commutative ring that is a graded complete intersection are proposed for a noncommutative graded $k$-algebra; these notions are justified by examples from noncommutative invariant theory.
A general overview of the existing difference ring theory for symbolic summation is given. Special emphasis is put on the user interface: the translation and back translation of the corresponding representations within the term algebra and…
Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…
We explore the connections between the linear algebra of symmetric matrices over GF(2) and the circuit theory of 4-regular graphs. In particular, we show that the equivalence relation on simple graphs generated by local complementation can…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…
The author has been interested in regions surrounded by cylinders of real algebraic hypersurfaces and their shapes and polynomials associated to them. Here, we formulate and investigate natural decompositions into such cylinders of real…
Let $X$ be a complex analytic manifold, $D\subset X$ a locally quasi-homogeneous free divisor, $E$ an integrable logarithmic connection with respect to $D$ and $L$ the local system of the horizontal sections of $E$ on $X-D$. In this paper…
We show a method in constructing algebraic cycles via intersection theory. It leads to a proof of the Lefschetz standard conjecture.
Let $Y$ be a smooth complete intersection of a quadric and a cubic in $\mathbb{P}^n$, with $n$ even. We show that $Y$ has a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence, the Chow ring of (powers…