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Projectivity of the moduli of equidimensional branchvarieties

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arxiv 2410.10753 v2 pith:ZSHM5CU6 submitted 2024-10-14 math.AG

Daniel Halpern-Leistner , Andres Fernandez Herrero , Trevor Jones , Ritvik Ramkumar This is my paper · ORCID
classification math.AG
keywords equidimensionalmodulibranchvarietiesprojectivityalexeev-knutsonampleapplicationcase
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We resolve an open problem posed by Alexeev-Knutson on the projectivity of the moduli of branchvarieties in the equidimensional case. As an application, we construct projective moduli spaces of reduced equidimensional varieties equipped with ample linear series and subject to a semistability condition.

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  1. Hassett--Keel Program in genus four

    math.AG 2025-04 accept novelty 8.0 of 10

    The full Hassett-Keel program for genus four is established, with explicit wall crossings and moduli stacks for all log canonical models of M4.

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