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Residues and Hyperfunctions
We discuss relative Čech-de Rham and relative Čech-Dolbeault cohomologies and their applications. In the de Rham case, we are mainly concerned with...
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Stratifications of real vector spaces from constructible sheaves with conical microsupport
Interpreting the syzygy theorem for tame modules over posets in the setting of derived categories of subanalytically constructible sheaves proves two...
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The moduli stack of principal \(\rho \)-sheaves and Gieseker–Harder–Narasimhan filtrations
Let X be a smooth projective variety and let G be a connected reductive group, both defined over a field of characteristic 0. Given a faithful...
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On the Bogomolov–Gieseker inequality for tame Deligne–Mumford surfaces
We generalize the Bogomolov–Gieseker inequality for semistable coherent sheaves on smooth projective surfaces to smooth Deligne–Mumford surfaces. We...
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Klyachko Diagrams of Monomial Ideals
In this paper, we introduce the notion of a Klyachko diagram for a monomial ideal I in a certain multi-graded polynomial ring, namely the Cox ring R ...
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Spectrum of a linear differential equation with constant coefficients
In this paper we compute the spectrum, in the sense of Berkovich, of an ultrametric linear differential equation with constant coefficients, defined...
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Group ring valued Hilbert modular forms
In this paper, we study the action of diamond operators on Hilbert modular forms with coefficients in a general commutative ring. In particular, we...
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Canonical Stratifications Along Bisheaves
A theory of bisheaves has been recently introduced to measure the homological stability of fibers of maps to manifolds. A bisheaf over a topological...
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Bounds for the stalks of perverse sheaves in characteristic p and a conjecture of Shende and Tsimerman
We prove a characteristic p analogue of a result of Massey which bounds the dimensions of the stalks of a perverse sheaf in terms of certain...
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Converse of \(L^2\) Existence and Extension of Cohomology Classes
The present paper grew out of my talk at Hayama conference in 2022. We give a survey of recent progress on a converse of...
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Bilinear forms with trace functions over arbitrary sets and applications to Sato-Tate
We prove non-trivial upper bounds for general bilinear forms with trace functions of bountiful sheaves, where the supports of two variables can be...
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Nadel-type multiplier ideal sheaves on complex spaces with singularities
In this article, we introduce multiplier ideal sheaves on complex spaces with singularities ( not necessarily normal) via Ohsawa’s extension measure,...
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On BV supermanifolds and the super Atiyah class
We study global and local geometry of forms on odd symplectic BV supermanifolds, constructed from the total space of the bundle of 1-forms on a base...
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Hodge numbers of O’Grady 6 via Ngô strings
We give an alternative computation of the Betti and Hodge numbers for manifolds of OG 6 type using the method of Ngô Strings introduced by de Cataldo,...
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