We discuss the isomorphism problem of projective schemes; given two projective schemes, can we algorithmically decide whether they are isomorphic? We give affirmative answers in the case of one-dimensional projective schemes, the case of smooth irreducible varieties with a big canonical sheaf or a big anti-canonical sheaf, and the case of K3 surfaces with a finite automorphism group. As related algorithmic problems, we also discuss decidability of positivity properties of invertible sheaves, and approximation of the nef cone and the pseudo-effective cone.

中文翻译：

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射影格式的同构问题及相关算法问题

我们讨论射影格式的同构问题；给定两个投影方案，我们可以通过算法确定它们是否同构吗？对于一维射影格式、具有大规范束或大反规范束的光滑不可约簇的情况以及具有有限自同构群的 K3 表面的情况，我们给出了肯定的答案。作为相关的算法问题，我们还讨论了可逆滑轮正性质的可判定性，以及nef锥和伪有效锥的近似。