The isomorphism problem of projective schemes and related algorithmic problems

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.

arXiv comment31 pages, v2: minor revision

References in corpus (6)

• Boundedness of pluricanonical maps of varieties of general type
• A characteristic free criterion of birationality
• Computing Global Extension Modules for Coherent Sheaves on a Projective Scheme
• Computing Néron-Severi groups and cycle class groups
• Automorphisms mapping a point into a subvariety
• Divisor package for Macaulay2