度量下降与保秩收缩

度量下降与保秩收缩

Metric descent and rank-preserving contractions

OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。

具体内容

稿件从光滑射影复簇上的光滑半正反典范度量出发，借助正规等维环面模型与指数零处的全一般伴随秩一条件，在修正后的反典范线上构造无权重可积半正度量，其显式有理边界修正拉回到例外除子。作者还讨论无正次数全纯形式的簇上的双度量转移，并声称在此类簇上一般截面与伴随秩假设可给出保持条件的收缩，除非已存在不变整体截面。

• 由光滑半正反典范度量构造修正反典范线上的可积半正度量
• 显式有理边界修正拉回到例外除子
• 在无正次数全纯形式的簇上讨论双度量转移与不变收缩

AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。

英文原始摘要

From a smooth semipositive anticanonical metric on a smooth projective complex variety, we construct an unweighted integrable semipositive metric on a corrected anticanonical line of a smooth base, using a normal equidimensional toroidal model and full generic adjoint rank one at exponent zero. The explicit rational boundary correction pulls back to an exceptional divisor. On varieties without positive-degree holomorphic forms, two-metric transfer gives sections with prescribed boundary poles from a finite-volume log-anticanonical metric and a target line with bounded semipositive weights. In particular, a smooth projective complex variety with a smoothly semipositive anticanonical bundle and no such forms has a nonzero invariant section of a positive anticanonical multiple for every torus action with its natural linearization. On this class of varieties, generic section and adjoint-rank hypotheses give contractions of invariant fibrations that preserve both conditions unless an invariant global section already exists.

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