OpenAI reports numerical semiampleness for nef Kähler adjoint classes

On a smooth connected compact Kähler manifold, if B is an effective rational simple-normal-crossing divisor with coefficients below one, M is a nef rational line bundle, K_X+B is pseudo-effective, and K_X+B+M is nef, then its real Bott–Chern first Chern class is represented by a semiample rational line bundle.

Curated contributions 1

Understand the problem ↓

OpenAI reports numerical semiampleness for nef Kähler adjoint classes

  • Mathematics

On a smooth connected compact Kähler manifold, if B is an effective rational simple-normal-crossing divisor with coefficients below one, M is a nef rational line bundle, K_X+B is pseudo-effective, and K_X+B+M is nef, then its real Bott–Chern first Chern class is represented by a semiample rational line bundle.

AI involvementAI-led
ImportanceNotable
Technical verificationReported
Human understandingFew

Understanding the problem

Read the background

On a smooth connected compact Kähler manifold, if B is an effective rational simple-normal-crossing divisor with coefficients below one, M is a nef rational line bundle, K_X+B is pseudo-effective, and K_X+B+M is nef, then its real Bott–Chern first Chern class is represented by a semiample rational line bundle.

Why it matters

If correct, proves numerical semiampleness of a broad class of nef adjoint classes on compact Kähler manifolds.

What counts as progress

Is a nef Kähler adjoint class numerically represented by a semiample line bundle under the stated assumptions?

Website timeline

Publication dates and editorial changes.