A guide to moduli theory beyond GIT

DOI10.1090/conm/803/16100zbMATH Open1547.14012MaRDI QIDQ6607622

Alfonso Zamora, Andres Fernandez Herrero, Tomás L. Gómez

Publication date: 18 September 2024

zbMATH Keywords

stacksmoduli spacesHarder-Narasimhan filtrationprincipal bundlesGieseker stabilitygood moduli spaces\(\Theta\)-stratificationsintrinsic GITprincipal \(\rho\)-sheaves

Mathematics Subject Classification ID

Vector bundles on surfaces and higher-dimensional varieties, and their moduli (14J60) Geometric invariant theory (14L24) Algebraic moduli problems, moduli of vector bundles (14D20) Stacks and moduli problems (14D23) Sheaves in algebraic geometry (14F06)

Cites Work

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• Quotients by groupoids
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• Versal deformations and algebraic stacks
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• On the moduli of vector bundles on an algebraic surface
• Moduli of stable sheaves. II
• Instability in invariant theory
• Moduli of representations of the fundamental group of a smooth projective variety. I
• Schematic Harder-Narasimhan stratification for families of principal bundles in higher dimensions
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• Semistable principal bundles. II: Positive characteristics
• Stable principal bundles on a compact Riemann surface
• Harder-Narasimhan reduction for principal bundles over a compact Kähler manifold
• Semistable principal bundles. I: Characteristic zero.
• Openness of K-semistability for Fano varieties
• A Luna étale slice theorem for algebraic stacks
• Reductivity of the automorphism group of K-polystable Fano varieties
• Schematic Harder-Narasimhan stratification for families of principal bundles and \(\lambda\)-modules
• A GIT interpretation of the Harder-Narasimhan filtration
• Principal bundles on projective varieties and the Donaldson-Uhlenbeck compactification
• Moduli space of principal sheaves over projective varieties
• Good moduli spaces for Artin stacks
• Space of unitary vector bundles on a compact Riemann surface
• The irreducibility of the space of curves of a given genus
• Algebraic spaces
• Lectures on the Moduli Stack of Vector Bundles on a Curve
• SCHEMATIC HARDER–NARASIMHAN STRATIFICATION
• Adequate moduli spaces and geometrically reductive group schemes
• Bounds for Behrend's Conjecture on the Canonical Reduction
• Addendum to “Semistable reduction of 𝐺-bundles on curves”
• A Stratification of the Null Cone Via the Moment Map
• Geometric Invariant Theory
• An Introduction to Moduli Stacks, with a View towards Higgs Bundles on Algebraic Curves
• Hilbert-Mumford stability on algebraic stacks and applications to $\mathcal{G}$-bundles on curves
• The Yang-Mills equations over Riemann surfaces
• Harder–Narasimhan reduction of a principal bundle
• Semistable reduction for $G$-bundles on curves
• Projectivity of the moduli space of vector bundles on a curve
• Algebraic stacks
• The moduli stack of principal \(\rho \)-sheaves and Gieseker-Harder-Narasimhan filtrations

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