AI 中文总结
本文建立klt伴随叶状曲面的极小模型程序，证明满足条件的ε-lc伴随叶状曲面构成有界族，应用于一般类型伴随叶状曲面，还得到秩1叶状结构典范除子体积的离散性结果。
AI 中文摘要
我们建立了klt伴随叶状曲面的极小模型程序，并将其用于研究极化伴随叶状曲面的有界性。我们证明，若ε-lc伴随叶状曲面的伴随典范除子是内省的，且存在内省且大的整极化子，同时它们的和的体积有上界，则这类曲面构成有界族。作为应用，我们建立了一般类型伴随叶状曲面的有界性和有效双有理性，还给出了其体积的统一正下界。最后，对于ε-lc Calabi-Yau伴随叶状曲面，我们证明其底面上秩1叶状结构的典范除子体积属于一个固定离散集合。
英文摘要
We establish the minimal model program for klt adjoint foliated surfaces and use it to study the boundedness of polarized adjoint foliated surfaces. We prove that $ε$-lc adjoint foliated surfaces with nef adjoint canonical divisor and a nef and big integral polarization form a bounded family, provided that the volume of their sum is bounded from above. As applications, we establish boundedness and effective birationality for adjoint foliated surfaces of general type, as well as a uniform positive lower bound for their volumes. Finally, for $ε$-lc Calabi--Yau adjoint foliated surfaces, we prove that the volumes of the canonical divisors of rank one foliations on the underlying surfaces belong to a fixed discrete set.
Comments50 pages. Comments are very welcome!
