A characterization of quasi-homogeneous Gorenstein surface singularities
A class of non-rational surface singularities with bijective Nash map
Let be a germ of complex analytic normal surface. On its minimal resolution, we consider the reduced exceptional divisor and its irreducible components , . The Nash map associates to each irreducible component of the space of arcs through on the unique component of cut by the strict transform of the generic arc in . Nash proved its injectivity and asked if it was bijective. As a particular case of our main theorem, we prove that this is the case if for any .
A Geometric Algebraicity Property for Moduli Spaces of Compact Kähler Manifolds with h 2, 0 = 1.
A natural equivalence relation on singularities
A new proof of desingularization over fields of characteristic zero.
We present a proof of embedded desingularization for closed subschemes which does not make use of Hilbert-Samuel function and avoids Hironaka's notion of normal flatness (see also [171 page 224). Given a subscheme defined by equations, we prove that embedded desingularization can be achieved by a sequence of monoidal transformations; where the law of transformation on the equations defining the subscheme is simpler then that used in Hironaka 's procedure. This is done by showing that desingularization...
A propos du problème des arcs de Nash
Soit la décomposition canonique de l’espace des arcs passant par une singularité normale de surface. Dans cet article, on propose deux nouvelles conditions qui si elles sont vérifiées permettent de montrer que n’est pas inclus dans . On applique ces conditions pour donner deux nouvelles preuves du problème de Nash pour les singularités sandwich minimales.
A residue formula for the index of a holomorphic flow.
An example of a non-projective smooth compactification of C3 with second Betti number equal to one.
Arc-analytic functions.
Auflösung der Entartungen holomorpher Abbildungen zwischen zweidimensionalen Mannigfaltigkeiten.