The 'corrected Durfee's inequality' for homogeneous complete intersections

2011/11/06 by Kerner, Dmitry, Nemethi, Andras
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1111.1411

Abstract

We address the conjecture of [Durfee1978], bounding the singularity genus, p_g, by a multiple of the Milnor number, μ, for an n-dimensional isolated complete intersection singularity. We show that the original conjecture of Durfee, namely (n+1)!p_g≤ μ, fails whenever the codimension r is greater than one. Moreover, we propose a new inequality, and we verify it for homogeneous complete intersections. In the homogeneous case the inequality is guided by a `combinatorial inequality', that might have an independent interest.

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