The full Hassett-Keel program for genus four is established, with explicit wall crossings and moduli stacks for all log canonical models of M4.
Projectivity of the moduli of equidimensional branchvarieties
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abstract
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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Hassett--Keel Program in genus four
The full Hassett-Keel program for genus four is established, with explicit wall crossings and moduli stacks for all log canonical models of M4.