Related papers: Constructing virtual Euler cycles and classes
In this paper, we investigate the local Euler obstruction and the relative local Euler obstruction in terms of constructible complexes of sheaves, characteristic cycles, and vanishing cycles. The fundamental tool that we use is the notion…
We construct an Euler system attached to a weight 2 modular form twisted by a Groessencharacter of an imaginary quadratic field, and apply this to bounding Selmer groups.
In this article we are examining extensions and some basic diagrammatic properties of modules, in both cases from a new, "virtual" point of view. As natural background for investigating the kind of problems we are dealing with, the virtual…
We enumerate total cyclic orders on $\left\{1,\ldots,n\right\}$ where we prescribe the relative cyclic order of consecutive triples $(i,{i+1},{i+2})$, these integers being taken modulo $n$. In some cases, the problem reduces to the…
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…
We give a construction of contact homology in the sense of Eliashberg--Givental--Hofer. Specifically, we construct coherent virtual fundamental cycles on the relevant compactified moduli spaces of pseudo-holomorphic curves.
We give a method to construct stable vector bundles whose rank divides the degree over curves of genus bigger than one. The method complements the one given by Newstead. Finally, we make some systematic remarks and observations in…
I employ methods from derived algebraic geometry to give a uniform moduli-theoretic construction of special cycle classes on integral models many Shimura varieties of Hodge type, including unitary, quaternionic, and orthogonal Shimura…
We determine the topological Euler number of certain moduli space of 1-dimensional closed subschemes in a smooth projective variety which admits a Zariski-locally trivial fibration with 1-dimensional fibers. The main approach is to use…
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…
We define complete stable pairs on a smooth projective variety, and construct their moduli space. These moduli spaces have natural morphisms to the moduli of stable pairs and Quot-schemes. As an example, we show that the moduli of complete…
We consider the Euler approach to construction and to investigation of the superintegrable systems related to the addition theorems. As an example we reconstruct Drach systems and get some new two-dimensional superintegrable Stackel…
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.
The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.
We can define a module to be an exact functor on a small abelian category. This is explained and shown to be equivalent to the usual definition but it does offer a different perspective, inspired by the notions from model theory of…
We introduce the tautological rings of moduli stacks of twisted curves and establish some basic properties.
We provide an account of the construction of the moduli stack of elliptic curves as an analytic orbifold. While intimately linked to Thurston's point of view on the subject (discrete groups acting properly and effectively on differentiable…
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…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
Basic facts and definitions of conformal moduli of rings and quadrilaterals are recalled. Some computational methods are reviewed. For the case of quadrilaterals with polygonal sides, some recent results are given. Some numerical…