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The generically nef tangent bundle conjecture for nef anticanonical manifolds
About 18 years old
Generically nef tangent bundle conjecture.
opennef-anticanonical-divisors rational-connectedness tangent-bundles
08
The nef anticanonical Albanese submersion conjecture
At least 17 years old
Albanese submersion conjecture. The Albanese map of $X$ is a surjective submersion.
openalbanese-maps complex-geometry nef-anticanonical-divisors
010