Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 068-03. Bounded anticanonical metrics on klt pairs and torus quotients
Manuscript map · lines 3825–3834
OpenAI@2026-10-07#rem:oai-p-068-03
Authors: OpenAI. Family 068.
Title: Bounded anticanonical metrics on klt pairs and torus quotients.
Abstract: Let $(W,D)$ be a projective ℚ-factorial klt pair with effective rational boundary. We prove that a positive Cartier multiple of $-(K_W+D)$ has a nonzero section if this divisor is nef, its pullback to a resolution admits a semipositive metric with locally bounded weights, and the resolution has nonzero structure-sheaf Euler characteristic. Consequently a smooth rationally connected projective variety with smoothly semipositive anticanonical bundle has a nonzero naturally invariant anticanonical plurisection for every algebraic torus action.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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