Related papers: A young person's guide to mixed Hodge modules
The notion of crossed modules for Lie 2-algebras is introduced. We show that, associated to such a crossed module, there is a strict Lie 3-algebra structure on its mapping cone complex and a strict Lie 2-algebra structure on its…
The article provides a brief survey of the mathematics of some of the newly being developed so called "hybrid" (also called "multi-physics" or "multi-wave") imaging techniques.
These notes are a brief introduction to the RSA algorithm and modular arithmetic. They are intended for an undergraduate audience.
In this expository note, we offer an overview of the relationship between Hodge-theoretic and geometric compactifications of moduli spaces of algebraic varieties.
The purpose of this paper is to introduce Hom-prealternative superalgebras and their bimodules. Some constructions of Hom-prealternative superalgebras and Hom-alternative superalgebras are given, and their connection with Hom-alternative…
A brief introduction to exterior differential systems for graduate students familiar with manifolds and differential forms. For complete files, see https://github.com/Ben-McKay/introduction-to-exterior-differential-systems
A construction of braid group actions on coherent sheaves using mixed Hodge modules and some well known constructions from geometric representation theory is given.
Generalizing a theorem of Macdonald, we show a formula for the mixed Hodge structure on the cohomology of the symmetric products of bounded complexes of mixed Hodge modules by showing the existence of the canonical action of the symmetric…
We count the number of submodules of an arbitrary module over a countable noetherian commutative ring. We give, along the way, a structural description of meager modules, which are defined as those that do not have the square of a simple…
We introduce a perfect discrete Morse function on the moduli space of a polygonal linkage. The ingredients of the construction are: (1) the cell structure on the moduli space, and (2) the discrete Morse theory approach, which allows to…
We present the rudiments of the Morita theory of module systems (over semirings), paralleling the classical Morita theory over associative rings.
We present in this article a general approach (in the form of recommendations and guidelines) for tackling Diophantine equation problems (whether single equations or systems of simultaneous equations). The article should be useful in…
Let $\textbf{H} = ((H, F^{\bullet}), L)$ be a polarized variation of Hodge structure on a smooth quasi-projective variety $U.$ By M. Saito's theory of mixed Hodge modules, the variation of Hodge structure $\textbf{H}$ can be viewed as a…
We survey recent work on moduli spaces of manifolds with an emphasis on the role played by (stable and unstable) homotopy theory. The theory is illustrated with several worked examples.
In this paper, we mainly focus on formal deformation theory of module homomorphisms. We first introduce the cohomology of module homomorphisms and study formal one-parameter deformation. We obtain some properties about obstructions. Then we…
The theory of modular deformations is generalized for the category of complex analytic polyhedra which includes germs of complex space as well as any compact complex analytic space. The objective of the theory is a construction of fine…
We discuss variations of mixed Hodge structure arising from projective morphisms of complex analytic spaces. Then we treat generalizations of Koll\'ar's torsion-free theorem, vanishing theorem, and so on, for reducible complex analytic…
We discuss the variations of mixed Hodge structure for cohomology with compact support of quasi-projective simple normal crossing pairs. We show that they are graded polarizable admissible variations of mixed Hodge structure. Then we prove…
We study the class of equimultiple modules. In particular, we prove several criteria for an equimultiple module to be a complete intersection and prove the openness of the equimultiple locus of an ideal module.
We study the local cohomology modules for the secant variety of lines of a smooth projective variety $Y$ and for higher secant varieties of smooth projective curves. We show that the local cohomological defect in the first case is related…