The moduli stack of principal $$\rho $$-sheaves and Gieseker–Harder–Narasimhan filtrations

Gómez, Tomás L.; Herrero, Andres Fernandez; Zamora, Alfonso

doi:10.1007/s00209-024-03497-6

Math. Z.

2024

DOI: 10.1007/s00209-024-03497-6

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The moduli stack of principal $$\rho $$-sheaves and Gieseker–Harder–Narasimhan filtrations

Tomás L. Gómez,

Andres Fernandez Herrero,

Alfonso Zamora

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2024

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A guide to moduli theory beyond GIT

Gómez,

Fernández Herrero,

Zamora

2024

Moduli Spaces and Vector Bundles—New Trends

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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 \Theta -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 \rho -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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A guide to moduli theory beyond GIT

Gómez,

Fernández Herrero,

Zamora

2024

Moduli Spaces and Vector Bundles—New Trends

View full text Add to dashboard Cite

show abstract

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The moduli stack of principal $$\rho $$-sheaves and Gieseker–Harder–Narasimhan filtrations

Cited by 1 publication

References 36 publications

A guide to moduli theory beyond GIT

A guide to moduli theory beyond GIT

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