RationalMaps, a package for Macaulay2

Bott, C. J.; Hassanzadeh, Seyed Hamid; Schwede, Karl

doi:10.48550/arxiv.1908.04337

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Positivity Of Invertible Sheaves1

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2021

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“…For each n, we can algorithmically check whether the map Φ L n is birational, see [Sim04,DHS12]. See also [BHSS19] for implementation of such an algorithm. Thus, bigness of an invertible sheaf is semi-decidable.…”

Section: Positivity Of Invertible Sheavesmentioning

confidence: 99%

The isomorphism problem of projective schemes and related algorithmic problems

Yasuda¹

2021

Preprint

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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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Section: Positivity Of Invertible Sheavesmentioning

confidence: 99%