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Graded Betti numbers of the Jacobian algebra and total Tjurina numbers of plane curves

Published 13 Jan 2026 in math.AG and math.AC | (2601.08583v1)

Abstract: In this paper we compute explicit closed formulas for the total Tjurina number $τ(C)$ of a reduced projective plane curve $C$ in terms of the graded Betti numbers of the corresponding Jacobian algebra. This yields in particular a completely new view point on the classical upper bounds for the total Tjurina number $τ(C)$ of a plane curve $C$ given by A. du Plessis and C. T. C. Wall.

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