A characterization of quasi-homogeneous Gorenstein surface singularities
A Counterexample to a Conjecture of Zariski.
A counterexample to the theorem of Beppo Levi in three dimensions.
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 note on ...-constant families of plane curves.
A problem of Kollár and Larsen on finite linear groups and crepant resolutions
The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calabi–Yau varieties. In this paper, we solve a problem raised by J. Kollár and M. Larsen on the structure of finite irreducible linear groups generated by elements of age . More generally, we bound the dimension of finite irreducible linear groups generated by elements of bounded deviation. As a consequence...
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 regulator map for surfaces with an isolated singularity
A resolution theorem for homology cycles of real algebraic varieties.
A simpler proof of toroidalization of morphisms from 3-folds to surfaces
We give a simpler and more conceptual proof of toroidalization of morphisms of 3-folds to surfaces, over an algebraically closed field of characteristic zero. A toroidalization is obtained by performing sequences of blow ups of nonsingular subvarieties above the domain and range, to make a morphism toroidal. The original proof of toroidalization of morphisms of 3-folds to surfaces is much more complicated.
A simplified proof of desingularization and applications.
This paper contains a short and simplified proof of desingularization over fields of characteristic zero, together with various applications to other problems in algebraic geometry (among others, the study of the behavior of desingularization of families of embedded schemes, and a formulation of desingularization which is stronger than Hironaka's). Our proof avoids the use of the Hilbert-Samuel function and Hironaka's notion of normal flatness: First we define a procedure for principalization of...
A simply connected surface of general type with pg = 0.
A Smooth Four-Dimensional G-Hilbert Scheme
2000 Mathematics Subject Classification: 14C05, 14L30, 14E15, 14J35.When the cyclic group G of order 15 acts with some specific weights on affine four-dimensional space, the G-Hilbert scheme is a crepant resolution of the quotient A^4 / G. We give an explicit description of this resolution using G-graphs.
A standard basis approach to syzygies of canonical curves.
A theorem on normal flatness
A vanishing theorem concerning the Artin component of a rational surface singularity.
Additive vector fields, algebraicity and rationality.
Algebraic Cycles on Certain Desingularized Nodal Hypersurfaces.
Altérations de variétés algébriques
Ample line bundles on blown up surfaces.