3 problems

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Esnault's finite-fundamental-group conjecture for Kähler manifolds
Esnault's conjecture. If
Conjecturesolvedfundamental-groups kahler-geometry symmetric-differentialsarXiv posted 2 days ago
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The symmetric differential nonvanishing conjecture for cotangent bundles
Symmetric differential nonvanishing conjecture. The cotangent bundle is pseudoeffective if and only if there exists a positive integer $m$ such that
Conjectureopencotangent-bundles pseudoeffectivity symmetric-differentialsarXiv posted 2 days ago
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Genericity conjecture for the favorable spectral-data locus
Let $X$ be an algebraic surface, and let $\mathscr B_X^{\Diamond}(k)$ be the distinguished subset of the postulated Hitchin base $\mathscr B_X(k)$ defined in the surrounding discus…
Conjectureopenalgebraic-surfaces hitchin-fibration symmetric-differentialsarXiv posted 2 days ago

Esnault's finite-fundamental-group conjecture for Kähler manifolds