Noncommutative unfolding of hypersurface singularity

MULTIPLIER IDEALS, b-FUNCTION, AND SPECTRUM OF A HYPERSURFACE SINGULARITY

We prove that certain roots of the Bernstein-Sato polynomial (i.e. b-function) are jumping coefficients up to a sign, showing a partial converse of a theorem of L. Ein, R. Lazarsfeld, K.E. Smith, and D. Varolin. We also prove that certain roots are determined by a filtration on the Milnor cohomology, generalizing a theorem of B. Malgrange in the isolated singularity case. This implies a certain...

2 00 1 On Hypersurface Quotient Singularity of Dimension 4

We consider geometrical problems on Gorenstein hypersurface orbifolds of dimension n ≥ 4 through the theory of Hilbert scheme of group orbits. For a linear special group G acting on C n , we study the G-Hilbert scheme, Hilb(C n ), and crepant resolutions of C n /G for G=the A-type abelian group Ar(n). For n = 4, we obtain the explicit structure of Hilb r(C 4 ). The crepant resolutions of C 4 /G...

0 On Hypersurface Quotient Singularity of Dimension 4

We consider geometrical problems on Gorenstein hypersurface orbifolds of dimension n ≥ 4 through the theory of Hilbert scheme of group orbits. For a linear special group G acting on C n , we study the G-Hilbert scheme, Hilb(C n ), and crepant resolutions of C n /G for G=the A-type abelian group Ar(n). For n = 4, we obtain the explicit structure of Hilb r(C 4 ). The crepant resolutions of C 4 /G...

An Index Theorem for Modules on a Hypersurface Singularity

A topological interpretation of Hochster’s Theta pairing of two modules on a hypersurface ring is given in terms of linking numbers. This generalizes results of M. Hochster and proves a conjecture of J. Steenbrink. As a corollary we get that the Theta pairing vanishes for isolated hypersurface singularities in an odd number of variables, as was conjectured by H. Dao. 2000 Math. Subj. Class. 32S...

Ricci Curvature Decay near a Real Hypersurface Singularity