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A Sheaf-Theoretic Construction of Shape Space
We present a sheaf-theoretic construction of shape space—the space of all shapes. We do this by describing a homotopy sheaf on the poset category of...
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Completeness of derived interleaving distances and sheaf quantization of non-smooth objects
We develop sheaf-theoretic methods to deal with non-smooth objects in symplectic geometry. We show the completeness of a derived category of sheaves...
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A Topological View of Sheaf Cohomology
In Sect. 9.3 we introduced algebraic topology informally, as the way to associate to topological...
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Sheaf homology of hyperplane arrangements, Boolean covers and exterior powers
We compute the sheaf homology of the intersection lattice of a hyperplane arrangement with coefficients in the graded exterior sheaf
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The Kawamata–Viehweg–Nadel-type vanishing theorem and the asymptotic multiplier ideal sheaf
In this paper we establish a Nadel-type vanishing theorem and a Kawamata–Viehweg-type vanishing theorem concerning the asymptotic multiplier ideal...
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Geometric Invariants for a Class of Submodules of Analytic Hilbert Modules Via the Sheaf Model
Let \(\Omega \subseteq {\mathbb {C}}^m\) be a bounded connected open...
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The Cohomology of Locally Symmetric Spaces
We discuss how automorphic representation theory controls the cohomology of arithmetic locally symmetric spaces.
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The generic equivalence among the Lipschitz saturations of a sheaf of modules
In this work, we extend the concept of the Lipschitz saturation of an ideal to the context of modules in some different ways, and we prove they are...
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Constructible Sheaf Complexes in Complex Geometry and Applications
We present a detailed introduction of the theory of constructible sheaf complexes in the complex algebraic and analytic setting. All concepts are...
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The Semi-infinite Intersection Cohomology Sheaf-II: The Ran Space Version
This chapter is a sequel to [Ga1]. We define the semi-infinite category on the Ran version of the affine Grassmannian and study a particular object...
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On sheaf cohomology and natural expansions
In this survey paper, we present Čech and sheaf cohomologies—themes that were presented by Koszul at University of São Paulo (Faisceaux et...
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A Primer on Sheaf Cohomology
This chapter is a first modest step toward a link with the algebraic (i.e., cohomological) approach to hyperfunctions and microfunctions favored by...
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Sheaf Co-homology and Its Applications
Sheaf theory and sheaf co-homology are tools which are very efficiently used in topology, number theory, and algebraic geometry. Indeed, these have...
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Bundle-Convexity and Kernel Asymptotics on a Class of Locally Pseudoconvex Domains
A generalization of Grauert’s solution of the Levi problem for strongly pseudoconvex domains will be given. On a class of bounded locally...
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Finiteness of Cohomology for Pro-locally Proper Maps
We introduce a notion of proper morphism for schematic finite spaces and prove the analog of Grothendieck’s finiteness theorem for it. The techniques...
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Instanton sheaves on Fano threefolds
Generalizing the definitions originally presented by Kuznetsov and Faenzi, we study (possibly non locally free) instanton sheaves of arbitrary rank...
