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Bondal-Polishchuk Conjecture for a Smooth Projective Variety

Algebra · posed by Alexei Bondal, Alexander Polishchuk, 1993 · disproved

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Statement

Bondal and Polishchuk conjectured in 1993 that the braid group acts transitively on the set of full exceptional collections in a triangulated category. Chang, Haiden and Schroll disproved it for partially wrapped Fukaya categories, but no counterexample of the form Db(X)D^b(X) for a smooth projective variety was known. A particular weak Fano threefold provides one.

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  1. construction · #1

    Anya Nordskova, using ChatGPT 5.6

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai assisted
    — a person led the work and used a model along the way.

    The AI disclosure is carefully bounded and worth quoting in full: the model most significantly found numerous mistakes in earlier attempted constructions, leading to the successful modifications, and it located the reference containing the threefold used. The author states that it did not produce the actual counterexample and was not used to generate any of the text.

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