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Matrix factorizations of generic polynomials

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arxiv 2112.08864 v6 pith:IYUUMCRQ submitted 2021-12-16 math.AC math.AG

Daniel Erman This is my paper · ORCID
classification math.ACmath.AG
keywords genericmatrixpolynomialstrengthbuchweitz-greuel-schreyerconjecturedegreeerman
verification ladder T0 review T1 audit T2 compute T3 formal
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We prove that the Buchweitz-Greuel-Schreyer Conjecture on the minimal rank of a matrix factorization holds for a generic polynomial of given degree and strength. The proof introduces a notion of the secondary strength of a polynomial, and uses a variant of the ultraproduct technique of Erman, Sam, and Snowden.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Slice rank and partition rank of the determinant

    math.CO 2025-09 conditional novelty 8.0 of 10

    The determinant has slice rank n, partition rank at least log2(n)+1, and the 4x4 determinant has partition rank 3, giving the first unbounded separation between partition rank and analytic rank.

  2. A linear lower bound on the Ulrich complexity of hypersurfaces

    math.AG 2026-07 conditional novelty 7.0 of 10

    Smooth hypersurfaces of dimension n≥6 and degree d≥3 have Ulrich complexity at least roughly linear in n (n-1 or n-2, or F of half-dimension for smaller n).

  3. On the projective normality of Ulrich bundles on some low-dimensional varieties

    math.AG 2024-12 reject novelty 7.0 of 10

    For curves, surfaces with q=pg=0, and hypersurfaces of dimension 2 or 3, the paper gives criteria for when Ulrich bundles are projectively normal, with a likely error in the hypersurface determinant computation.

  4. Ranks of matrix factorizations and sheaf cohomology

    math.AG 2024-12 conditional novelty 6.0 of 10

    A graded Buchweitz-Greuel-Schreyer rank conjecture is shown equivalent to a new sheaf-cohomology lower bound on non-Fano hypersurfaces, with a new exact Betti-number-to-cohomology formula as the bridge.

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