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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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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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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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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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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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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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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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Sheaf-Theoretic Stratification Learning from Geometric and Topological Perspectives
We investigate a sheaf-theoretic interpretation of stratification learning from geometric and topological perspectives. Our main result is the...
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Constant Scalar Curvature Sasaki Metrics and Projective Bundles
In this paper we consider the Boothby-Wang construction over twist 1 stage 3 Bott orbifolds given in terms of the log pair...
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Stability of kernel sheaves associated to rank one torsion-free sheaves
We show the kernel sheaf associated to a sufficiently positive torsion-free sheaf of rank one is slope stable. Furthermore, we are able to give an...
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Existence and non-existence of constant scalar curvature and extremal Sasaki metrics
We discuss the existence and non-existence of constant scalar curvature, as well as extremal, Sasaki metrics. We prove that the natural...
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An Evertse–Ferretti Nevanlinna constant and its consequences
In this paper, we introduce the notion of an Evertse–Ferretti Nevanlinna constant and compare it with the birational Nevanlinna constant introduced...
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A Note on Real Line Bundles with Connection and Real Smooth Deligne Cohomology
We define a Real version of smooth Deligne cohomology for manifolds with involution which interpolates between equivariant sheaf cohomology and...