Related papers: Hypercovers in Differential Geometry
We show that the topological classification and the smooth classification are generically the same for certain families of plane curves in a semi-local case(the double local case). Especially we give the normal form of transversely jointed…
This article is a sequel to hep-th/9411050, q-alg/9412017, q-alg/9503013. Given a collection of $m$ finite factorizable sheaves $\{\CX_k\}$, we construct here some perverse sheaves over configuration spaces of points on a projective line…
By a theorem of Chevalley the image of a morphism of varieties is a constructible set. The algebraic version of this fact is usually stated as a result on "extension of specializations" or "lifting of prime ideals". We present a difference…
We prove that the projective model structure on the category of unbounded cochain complexes extends naturally to the category of contractions. The proof is completely elementary and we do not assume familiarity with model categories.
We consider generalized complete intersection manifolds in the product space of projective spaces, and work out useful aspects pertaining to the cohomology of sheaves over them. First, we present and prove a vanishing theorem on the…
A `discrete differential manifold' we call a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides us with a convenient framework for the formulation of…
Special generic maps are smooth maps at each singular point of which we can represent as $(x_1, \cdots, x_m) \mapsto (x_1,\cdots,x_{n-1},\sum_{k=n}^{m}{x_k}^2)$ for suitable coordinates. Morse functions with exactly two singular points on…
We expand the toolbox of (co)homological methods in computational topology by applying the concept of persistence to sheaf cohomology. Since sheaves (of modules) combine topological information with algebraic information, they allow for…
Pseudo-Riemannian metrics with Levi-Civita connection in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the maximal rank solutions of a certain overdetermined projectively…
We develop a local-to-global formalism for constructing Calabi-Yau structures for global sections of constructible sheaves or cosheaves of categories. The required data - an isomorphism of the sheafified Hochschild homology with the…
We generalize the higher Riemann-Hilbert correspondence in the presence of scalar curvature for a (possibly non-compact) smooth manifold $M$. We show that the dg-category of curved $\infty$-local systems, the dg-category of graded vector…
One generally expects that the techniques of arboreal singularities and gluing of local differential graded categories will result in a useful global invariant for all Weinstein manifolds. In this paper we construct explicit models for the…
We introduce a notion of stability for sheaves with respect to several polarisations that generalises the usual notion of Gieseker-stability. We prove, under a boundedness assumption, which we show to hold on threefolds or for rank two…
In this paper, we present a generalization of Grothendieck pretopologies -- suited for semicartesian categories with equalizers $C$ -- leading to a closed monoidal category of sheaves, instead of closed cartesian category. This is proved…
After explaining the importance of model categories in abstract homotopy theory, we provide concrete examples demonstrating that various categories of manifolds do not have all finite colimits, and hence cannot be model categories. We then…
Given a morphism $f: X \rightarrow S$ of complex algebraic varieties and a constructible sheaf $\mathcal{G}$ on $X$, we compute the local monodromy of $Rf_*(\mathcal{G})$ and $Rf_!(\mathcal{G})$ in terms of the local monodromy of…
We introduce a nonstandard extension of the category of diffeological spaces, and demonstrate its application to the study of generalized functions. Just as diffeological spaces are defined as concrete sheaves on the site of Euclidean open…
When a non-singular complex projective surface $X$ satisfies that $K_X\sim 0$, we shall show that there are only finitely many isomorphic classes as abstract schemes in the set of moduli scheme of $H$-semistable sheaves with fixed Chern…
The first part of this paper provides a new formulation of chiral differential operators (CDOs) in terms of global geometric quantities. The main result is a recipe to define all sheaves of CDOs on a smooth cs-manifold; its ingredients…
From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link…