TY - JOUR

T1 - Durfee-type bound for some non-degenerate complete intersection singularities

AU - Kerner, Dmitry

AU - Némethi, András

N1 - Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - The Milnor number, μ(X, 0) , and the singularity genus, pg(X, 0) , are fundamental invariants of isolated hypersurface singularities (more generally, of local complete intersections). The long standing Durfee conjecture (and its generalization) predicted the inequality μ(X, 0) ≥ (n+ 1) ! pg(X, 0) , here n= dim (X, 0). Recently we have constructed counterexamples, proposed a corrected bound and verified it for the homogeneous complete intersections. In the current paper we treat the case of germs with Newton-non-degenerate principal part when the Newton diagrams are “large enough”, i.e. they are large multiples of some other diagrams. In the case of local complete intersections we prove the corrected inequality, while in the hypersurface case we prove an even stronger inequality.

AB - The Milnor number, μ(X, 0) , and the singularity genus, pg(X, 0) , are fundamental invariants of isolated hypersurface singularities (more generally, of local complete intersections). The long standing Durfee conjecture (and its generalization) predicted the inequality μ(X, 0) ≥ (n+ 1) ! pg(X, 0) , here n= dim (X, 0). Recently we have constructed counterexamples, proposed a corrected bound and verified it for the homogeneous complete intersections. In the current paper we treat the case of germs with Newton-non-degenerate principal part when the Newton diagrams are “large enough”, i.e. they are large multiples of some other diagrams. In the case of local complete intersections we prove the corrected inequality, while in the hypersurface case we prove an even stronger inequality.

UR - http://www.scopus.com/inward/record.url?scp=84975318188&partnerID=8YFLogxK

U2 - 10.1007/s00209-016-1702-1

DO - 10.1007/s00209-016-1702-1

M3 - Article

AN - SCOPUS:84975318188

SN - 0025-5874

VL - 285

SP - 159

EP - 175

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 1-2

ER -