AI 中文总结
该研究证明每个复射影簇双有理等价于带cscK度量的光滑射影流形，通过解决Lefschetz pencil的基点轨迹构造cscK模型，还在二维情形证明了曲面爆破的cscK度量民间猜想。
AI 中文摘要
我们证明了每个复射影簇都双有理等价于一个容许常数量曲率Kähler（cscK）度量的光滑射影流形。对任意光滑射影簇，通过在足够丰富的线性系中解决一般Lefschetz pencil的余维2基点轨迹，可得到一个双有理cscK模型。cscK极化有明确表达式，即使初始簇不稳定也能生成cscK模型。在二维情形，这证明了民间猜想：任意复射影曲面在足够多点处的爆破都容许cscK度量。
英文摘要
We prove that every complex projective variety is birational to a smooth projective manifold admitting a constant scalar curvature Kähler (cscK) metric. For any smooth projective variety, a birational cscK model is obtained by resolving the codimension two base locus of a general Lefschetz pencil in a sufficiently positive linear system. The cscK polarization is given explicitly, producing a cscK model also when the initial variety is unstable. In dimension two this proves the folklore conjecture that the blowup of any complex projective surface in enough points admits cscK metrics.
Comments30 pages, comments very welcome
