相关论文: Notes on Perverse Sheaves and Vanishing Cycles
We consider a hyperplane arrangement in $\mathbb{C}^n$ defined over $\mathbb{R}$, and the associated natural stratification of $\mathbb{C}^n$. The category of perverse sheaves smooth with respect to this stratification was described by…
We aim to use the concept of sheaf to establish a link between certain aspects of the set of positive integers numbers, a topic corresponding to the elementary mathematics, and some fundamental ideas of contemporary mathematics. We hope…
Kapranov and schechtman gave quiver description of perverse sheaves on real hyperplane arrangements. We used this description to relate the perverse sheaves on Coxeter hyperplane arrangements of type $\mathcal A_n$ for different values of…
We consider a class of discontinuous piecewise linear differential systems in $\mathbb{R}^3$ with two pieces separated by a plane. In this class we show that there exist differential systems having: a unique limit cycle, a unique…
We discuss and prove a number of results for calculating characteristic cycles, or graded, enriched characteristic cycles. We concentrate particularly on results related to hypersurfaces.
This is a large audience version of our previous work (see math.AG/0301146) in which we prove the existence of an (exact) equivalence between the category of coherent analytic sheaves and the category of $\bar{\partial}$-coherent sheaves.…
Work in progress concerning alternative formalizations of arithmetic.
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
A brief summary of recent developments in mathematical diffraction theory is given. Particular emphasis is placed on systems with aperiodic order and continuous spectral components. We restrict ourselves to some key results and refer to the…
We present, to the best of the authors' knowledge, all known results for the (planar) crossing numbers of specific graphs and graph families. The results are separated into various categories; specifically, results for general graph…
Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic…
This paper reproves a general form of the Green-Lazarsfeld 'generic vanishing' theorem and more recent strengthenings, as well as giving some new applications.
A short note on the reverse mathematical status of the totality of the relativised fast growing hierarchy.
In these notes we provide the foundation for the deformation theoretic parts of arXiv:0807.3753 and arXiv:math/0102005.
The calculus of finite differences is a solid foundation for the development of operations such as the derivative and the integral for infinite sequences. Here we showed a way to extend it for finite sequences. We could then define…
In this paper, we describe a general theory of "spaces with structure sheaves." Specializations of this theory include the classical theory of schemes, the theory of Deligne-Mumford stacks, and their derived generalizations.
In this survey we overview known results and get several new results on digraph compositions which generalize several classes of digraphs, such as quasi-transitive digraphs. After an introductory section, the paper is divided into six…
In this paper a method of constructing a semiorthogonal decomposition of the derived category of $G$-equivariant sheaves on a variety $X$ is described, provided that the derived category of sheaves on $X$ admits a semiorthogonal…
We extend some of the results of Bondal-Orlov on the equivalence of derived categories to the case of orbifolds by using the category of coherent orbifold sheaves.
In this article we survey recent results of joint work with Lutz Hille on exceptional sequences of invertible sheaves on rational surfaces and give examples.