Calabi--Yau 对偶的有效锥猜想
代数几何
2026-02-17 v2
摘要
我们提出了关于klt Calabi--Yau 对偶(X,Δ)的有效锥猜想，涉及有效 divisors 锥Eff(X)相对于pseudo-automorphisms群PsAut(X,Δ)作用的结构。在假设存在良好的最小模型（在维数为3时已知成立）的前提下，我们证明了(X,Δ)的有效锥猜想等价于Kawamata--Morrison--Totaro可移动锥猜想。作为应用，我们证明了Schoen 通过Namikawa、Grassi和Morrison研究的光滑Calabi--Yau三维簇在无条件情况下满足可移动锥猜想。我们还表明，对于此类Calabi--Yau三维簇X，除X本身外，其所有最小模型都具有有理多面体nef锥。
引用
@article{arxiv.2406.07307,
title = {The effective cone conjecture for Calabi--Yau pairs},
author = {Cécile Gachet and Hsueh-Yung Lin and Isabel Stenger and Long Wang},
journal= {arXiv preprint arXiv:2406.07307},
year = {2026}
}
备注
v2: Theorem 6.1 is strengthened: The existence of good minimal models is now assumed only for specific varieties (see new Assumption 2.5) instead of every variety of a given dimension. The definition of the group $\mathrm{PsAut}(X,\Delta;f)$ is corrected, and the proofs of Lemmas 5.1, 5.2 are modified accordingly. Exposition is shortened and improved following the referees' feedback