On the isomorphism problem of projective schemes
Speaker: Takehiko Yasuda (Osaka University)

Time: 15h15, Friday, April 30, 2021

Session Chairs: Prof. Baohua Fu (MCM) and Prof. Yusuke Nakamura(University of Tokyo)

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Abstract: I will talk about the isomorphism problem of projective schemes; is it algorithmically decidable whether or not two given projective (or, more generally, quasi-projective) schemes, say over an algebraic closure of Q, are isomorphic? I will explain that it is indeed decidable for the following classes of schemes: (1) one-dimensional projective schemes, (2) one-dimensional reduced quasi-projective schemes, (3) smooth projective varieties with either the canonical divisor or the anti-canonical divisor being big, and (4) K3 surfaces with finite automorphism group. Our main strategy is to compute Iso schemes for finitely many Hilbert polynomials. I will also discuss related decidability problems concerning positivity properties (such as ample, nef and big) of line bundles.

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