3 problems

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Yau's positive holomorphic sectional curvature conjecture for rational and unirational manifolds
Yau's conjecture. Every rational or unirational manifold admits a Kähler metric with $H>0$ everywhere.
Conjectureopenholomorphic-sectional-curvature kahler-geometry rational-varietiesarXiv posted 3 days ago
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The rationality conjecture for components $C_{ijk}(m)$
Let $C_{ijk}(m)$ denote the irreducible components of $X(m,i)$ indexed by the stabilized component data. Rationality conjecture. All varieties $C_{ijk}(m)$ are rational. This is on…
Conjectureopenrational-varieties resultantal-varietiesarXiv posted 3 days ago
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Conjecture that smooth rational varieties are plain
Smooth rational varieties are plain. Every smooth and rational variety is plain.
Conjectureopenalgebraic-geometry birational-geometry rational-varietiesarXiv posted 3 days ago

Yau's positive holomorphic sectional curvature conjecture for rational and unirational manifolds