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arXiv · 2107.09277

The isomorphism problem of projective schemes and related algorithmic problems

Takehiko Yasuda
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Abstract

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.

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Takehiko Yasuda. 2021-12-27. The isomorphism problem of projective schemes and related algorithmic problems. https://doi.org/10.1142/s021819672350039x

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