相关论文: Harder-Narasimhan Filtrations and Zigzag Persisten…

We investigate a semi-continuity property for stability conditions for sheaves that is important for the problem of variation of the moduli spaces as the stability condition changes. We place this in the context of a notion of stability…

After making correct, and then improving, our definition of the category of irregular mixed Hodge modules thanks to Mochizuki's recent results arXiv:2108.03843, we show how these results allow us to obtain Kodaira-Saito-type vanishing…

Zigzag persistence is a powerful extension of the standard persistence which allows deletions of simplices besides insertions. However, computing zigzag persistence usually takes considerably more time than the standard persistence. We…

In this article we study chains of torsion classes in an abelian category $\mathcal{A}$. We prove that each chain of torsion classes induce a Harder-Narasimhan filtration for every nonzero object $M$ in $\mathcal{A}$, generalising a…

We generalize type $A$ quivers to continuous type $A$ quivers and prove initial results about pointwise finite-dimensional (pwf) representations. We classify the indecomosable pwf representations and provide a decomposition theorem,…

The Harder-Narasimhan theory provides a canonical filtration of a vector bundle on a projective curve whose successive quotients are semistable with strictly decreasing slopes. In this article, we present the formalization of…

Using subvarieties, which we call Demazure quiver varieties, of the quiver varieties of Nakajima, we give a geometric realization of Demazure modules of Kac-Moody algebras with symmetric Cartan data. We give a natural geometric…

We relate the representations of the rational Cherednik algebras associated with the complex reflection group G(m,1,n) to sheaves on Nakajima quiver varieties associated with extended Dynkin gaphs via a Z-algebra construction. As the…

For a stability condition $\sigma$ on a triangulated category, Dimitrov-Katzarkov introduced the notion of a $\sigma$-exceptional collection. In this paper, we study full $\sigma$-exceptional collections in the derived category of an…

We extend previous results on boundedness of sets of coherent sheaves on a compact K\"ahler manifold to the relative and not necessarily smooth case. This enlarged context allows us to prove properness properties of the relative Douady…

We formulate a theory of instability and Harder-Narasimhan filtrations for an arbitrary moduli problem in algebraic geometry. We introduce the notion of a $\Theta$-stratification of a moduli problem, which generalizes the Kempf-Ness…

We study persistence modules defined on commutative ladders. This class of persistence modules frequently appears in topological data analysis, and the theory and algorithm proposed in this paper can be applied to these practical problems.…

We interpret some results of persistent homology and barcodes (in any dimension) with the language of microlocal sheaf theory. For that purpose we study the derived category of sheaves on a real finite-dimensional vector space V. By using…

We review the notion of Gieseker stability for torsion-free Higgs sheaves. This notion is a natural generalization of the classical notion of Gieseker stability for torsion-free coherent sheaves. We prove some basic properties that are…

We investigate positive definiteness, Hurwitz stability and Schur stability of parametric interval matrices. We give a verifiable sufficient condition for positive definiteness of parametric interval matrices with non-linear dependencies.…

We show a strong Hamiltonian stability result for a simpler and larger distance on the Tamarkin category. We also give a stability result with support conditions.

This survey intends to present the basic notions of Geometric Invariant Theory (GIT) through its paradigmatic application in the construction of the moduli space of holomorphic vector bundles. Special attention is paid to the notion of…

Unstable holomorphic bundles can be described algebraically by Harder-Narasimhan filtrations. In this note we show how such filtrations correspond to the existence of special metrics defined by Hermitian-Einstein inequalities.

A fundamental challenge in multiparameter persistent homology is the absence of a complete and discrete invariant. To address this issue, we propose an enhanced framework that realizes a holistic understanding of a fully commutative…

We study the influence of side walls on the stability of falling liquid films. We combine a temporal biglobal stability analysis based on the linearized Navier-Stokes equations with experiments measuring the spatial growth rate of…