Ranks of matrix factorizations and sheaf cohomology

Published 2 Dec 2024 in math.AG and math.AC | (2412.01060v1)

Abstract: Buchweitz-Greuel-Schreyer conjectured in 1987 a lower bound on the ranks of matrix factorizations over certain local hypersurface rings. We study a graded version of this conjecture, and we show that it implies a novel conjecture concerning the cohomology of sheaves over non-Fano projective hypersurfaces.

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