On the Gieseker Harder–Narasimhan filtration for principal bundles

Biswas, Indranil; Zamora, Alfonso

doi:10.1016/j.bulsci.2015.02.004

Cited by 6 publications

(1 citation statement)

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“…There has been partial attempts to construct a filtration that accounts for all of the terms in the Hilbert polynomial in lower rank [Zam16]. On the other hand, in [BZ16] it was shown that the notion of Gieseker Harder-Narasimhan parabolic reduction cannot be related to the Gieseker-Harder-Narasimhan filtration of the underlying vector bundles for faithful representations, which meant that the main strategies in the literature (e.g. [AAB02]) could not possibly apply if we try to account for all terms of the Hilbert polynomial.…”

Section: Introductionmentioning

confidence: 99%

A guide to moduli theory beyond GIT

Gómez¹,

Herrero²,

Zamora³

2023

Preprint

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In this survey we provide an overview of some recent developments in the construction of moduli spaces using stack-theoretic techniques. We will also explain the analogue of Harder-Narasimhan stratifications for general stacks, known as Θ-stratifications. As an application of the ideas exposed here, we address the moduli problem of principal bundles over higher dimensional projective varieties, as well as its different compactifications by the so-called principal ρ-sheaves. We construct a stratification by instability types whose lower strata admits a proper good moduli space of "Gieseker semistable" objects and a new Gieseker-type Harder-Narasimhan filtration for these objects. Detailed proofs of the latter results will appear elsewhere.

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Section: Introductionmentioning

confidence: 99%

A guide to moduli theory beyond GIT

Gómez¹,

Herrero²,

Zamora³

2023

Preprint

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Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration

Zamora

Zúñiga-Rojas

2021

SpringerBriefs in Mathematics

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SpringerBriefs in Mathematicsshowcases expositions in all areas of mathematics and applied mathematics. Manuscripts presenting new results or a single new result in a classical field, new field, or an emerging topic, applications, or bridges between new results and already published works, are encouraged. The series is intended for mathematicians and applied mathematicians. All works are peer-reviewed to meet the highest standards of scientific literature.

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