The isomorphism problem of projective schemes and related algorithmic problems
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866913241978896384 |
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| author | Yasuda, Takehiko |
| author_facet | Yasuda, Takehiko |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_09277 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The isomorphism problem of projective schemes and related algorithmic problems Yasuda, Takehiko Algebraic Geometry 14Q15, 14Q10, 14Q05 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. |
| title | The isomorphism problem of projective schemes and related algorithmic problems |
| topic | Algebraic Geometry 14Q15, 14Q10, 14Q05 |
| url | https://arxiv.org/abs/2107.09277 |