An example concerning a question of Zariski
An example of a non-projective smooth compactification of C3 with second Betti number equal to one.
An explicit formula for period determinant
We consider a generic complex polynomial in two variables and a basis in the first homology group of a nonsingular level curve. We take an arbitrary tuple of homogeneous polynomial 1-forms of appropriate degrees so that their integrals over the basic cycles form a square matrix (of multivalued analytic functions of the level value). We give an explicit formula for the determinant of this matrix.
An inequality for symplectic fillings of the link of a hypersurface K3 singularity
Some relations between normal complex surface singularities and symplectic fillings of the links of the singularities are discussed. For a certain class of singularities of general type, which are called hypersurface K3 singularities in this paper, an inequality for numerical invariants of any minimal symplectic fillings of the links of the singularities is derived. This inequality can be regarded as a symplectic/contact analog of the 11/8-conjecture in 4-dimensional topology.
An obstruction for smoothing of Gorenstein surface singularities.
An Orlik-Solomon type algebra for matroids with a fixed linear class of circuits.
Analytic equivalence of plane curve singularities .
Analytic Subvarietis in Cn with Given Isolated Singularities.
Analyticité des conditions de Whitney strictes
Soient un espace analytique complexe réduit de dimension pure et un sous-espace lisse de de dimension pure tel que dimension dimension .L’ensemble des points de en lesquels les conditions de Whitney strictes ne sont pas satisfaites par est un sous-espace analytique propre de .
Analytische Hyperflächen mit vorgegebenen Singularitäten*.
Appendix to : “smoothings of cusp singularities via triangle singularities”
Approximation diophantienne dans les corps de séries en plusieurs variables
Nous montrons ici un théorème d’approximation diophantienne entre le corps des séries formelles en plusieurs variables et son complété pour la topologie de Krull.
Arc-analytic functions.
Are the Isolated Singularities of Complete Intersections Determined by Their Singular Subspaces?
Arithmetic Monodromy Groups.
Around the intersection form of an isolated singularity of hypersurface
Arrangements and Milnor fibres.
Asymptotic behaviour of numerical invariants of algebraic varieties
We show that if the degree of a nonsingular projective variety is high enough, maximization of any of the most important numerical invariants, such as class, Betti number, and any of the Chern or middle Hodge numbers, leads to the same class of extremal varieties. Moreover, asymptotically (say, for varieties whose total Betti number is big enough) the ratio of any two of these invariants tends to a well-defined constant.
Asymptotique des intégrales-fibres
Auflösung der Entartungen holomorpher Abbildungen zwischen zweidimensionalen Mannigfaltigkeiten.