The 'corrected Durfee's inequality' for homogeneous complete intersections
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\leq 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.
10 pages; final version; to appear in "Mathematische Zeitschrift"