TY - JOUR
T1 - The 'corrected Durfee's inequality' for homogeneous complete intersections
AU - Kerner, Dmitry
AU - Némethi, András
N1 - Funding Information:
A. Némethi is partially supported by OTKA Grant 100796 of the Hungarian Academy of Sciences.
PY - 2013/8/1
Y1 - 2013/8/1
N2 - We address the conjecture of Durfee (Math Ann 232:85-98, 1978), bounding the singularity genus pg 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)!· pg ≤ μ, fails whenever the codimension r is greater than one. Moreover, we propose a new inequality Cn,r · pg μ, 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.
AB - We address the conjecture of Durfee (Math Ann 232:85-98, 1978), bounding the singularity genus pg 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)!· pg ≤ μ, fails whenever the codimension r is greater than one. Moreover, we propose a new inequality Cn,r · pg μ, 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.
UR - http://www.scopus.com/inward/record.url?scp=84880602209&partnerID=8YFLogxK
U2 - 10.1007/s00209-012-1120-y
DO - 10.1007/s00209-012-1120-y
M3 - Article
AN - SCOPUS:84880602209
SN - 0025-5874
VL - 274
SP - 1385
EP - 1400
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 3-4
ER -