Invariants of plane algebraic curves via representations of the braid group.
Kodaira singularities and an extension of Arnold's strange duality
La correspondance de McKay
Letter to the Editors.
Local monomialization of transcendental extensions
Suppose that are regular local rings which are essentially of finite type over a field of characteristic zero. If is a valuation ring of the quotient field of which dominates , then we show that there are sequences of monoidal transforms (blow ups of regular primes) and along such that is a monomial mapping. It follows that a morphism of nonsingular varieties can be made to be a monomial mapping along a valuation, after blow ups of nonsingular subvarieties.
Local volumes of Cartier divisors over normal algebraic varieties
In this paper we study a notion of local volume for Cartier divisors on arbitrary blow-ups of normal complex algebraic varieties of dimension greater than one, with a distinguished point. We apply this to study an invariant for normal isolated singularities, generalizing a volume defined by J. Wahl for surfaces. We also compare this generalization to a different one arising in recent work of T. de Fernex, S. Boucksom, and C. Favre.
Modèle projectif régulier et désingularisation.
Modulflächen und Modulkurven zur symmetrischen Hilbertschen Modulgruppe
Monodromy conjecture for some surface singularities
Nakamaye’s theorem on log canonical pairs
We generalize Nakamaye’s description, via intersection theory, of the augmented base locus of a big and nef divisor on a normal pair with log-canonical singularities or, more generally, on a normal variety with non-lc locus of dimension . We also generalize Ein-Lazarsfeld-Mustaţă-Nakamaye-Popa’s description, in terms of valuations, of the subvarieties of the restricted base locus of a big divisor on a normal pair with klt singularities.
New Examples of Threefolds with c1 = 0.
Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs
Using non-Archimedian integration over spaces of arcs of algebraic varieties, we define stringy Euler numbers associated with arbitrary Kawamata log-terminal pairs. There is a natural Kawamata log-terminal pair corresponding to an algebraic variety having a regular action of a finite group . In this situation we show that the stringy Euler number of this pair coincides with the physicists’ orbifold Euler number defined by the Dixon-Harvey-Vafa-Witten formula. As an application, we prove a conjecture...
Normal cones and sheaves of relative jets
Normal degenerations of the complex projective plane.
Note on Resulution of Singularities of Embedded Algebraic Varieties.
On a Geometric Interpretation of Multiplicity.
On a Result of Riemenschneider.
On Analytic Abelian Coverings.
On blowing up versal discriminants
It is well-known that the versal deformations of nonsimple singularities depend on moduli. The first step in deeper understanding of this phenomenon is to determine the versal discriminant, which roughly speaking is an obstacle for analytic triviality of an unfolding or deformation along the moduli. The goal of this paper is to describe the versal discriminant of and singularities basing on the fact that the deformations of these singularities may be obtained as blowing ups of certain deformations...
On Compactification of Schemes.