5 problems

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The geometric Shafarevich conjecture for families of curves
Geometric Shafarevich conjecture. The set
Conjecturesolvedalgebraic-curves boundedness moduli-of-varietiesarXiv posted 2 days ago
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Boundedness conjecture for slc stable minimal models
Boundedness conjecture for slc stable minimal models. The family
Conjectureopenmoduli-of-varieties slc-singularities stable-minimal-modelsarXiv posted 2 days ago
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Relative Kähler–Einstein stability conjecture for families
Let $f:X\to B$ be a family admitting a relative Kähler–Einstein metric. A family is called stable in the sense of Alexeev and Kollár–Shepherd-Barron when it satisfies the correspon…
Conjectureopenkahler-einstein-metrics moduli-of-varieties stable-familiesarXiv posted 2 days ago
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The slope inequality conjecture for fibrations with mildly singular fibres
Slope inequality conjecture. Under these assumptions, the fibration satisfies the displayed slope inequality. The inequality is equivalent to the $f$ -positivity of $\omega_f$ and f…
Conjectureopenfibrations moduli-of-varieties slope-inequalitiesarXiv posted 2 days ago
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Shafarevich's hyperbolicity conjecture for canonically polarized varieties
Shafarevich's hyperbolicity conjecture. If $C$ parameterizes a non-isotrivial family of canonically polarized manifolds, then
Conjectureopenalgebraic-geometry hyperbolicity moduli-of-varietiesarXiv posted 2 days ago

5 problems

The geometric Shafarevich conjecture for families of curves

Boundedness conjecture for slc stable minimal models

Relative Kähler–Einstein stability conjecture for families

The slope inequality conjecture for fibrations with mildly singular fibres

Shafarevich's hyperbolicity conjecture for canonically polarized varieties