Remark: 068-02. Invariant anticanonical indices and conversion of twisted differentials

Authors: OpenAI. Family 068.

Title: Invariant anticanonical indices and conversion of twisted differentials.

Abstract: For a holomorphic action of a compact torus on a compact complex manifold, we prove that the invariant Euler characteristic of naturally linearized anticanonical powers is polynomial on a divisible progression, with its actual value at exponent zero. Independently, on a smooth projective variety with smoothly semipositive anticanonical bundle, we remove a fixed pseudoeffective error from an unbounded sequence of effective twists. These results convert invariant cohomology into twisted differential forms and prove anticanonical nonvanishing on smooth projective varieties with smoothly semipositive anticanonical bundle, by descending the forms before conversion.

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.