Equisingular Families of Plane Curves with Many Connected Components

Geometry of Obstructed Equisingular Families of Algebraic Curves and Hypersurfaces

One of the main achievements of the algebraic geometry of the 20th century was to realize that it is fruitful not only to study algebraic varieties by themselves but also in families. That means that one should consider the space classifying all varieties with given properties. These spaces are called moduli spaces. The advantage of algebraic geometry is that many times those spaces are themsel...

ZARISKI k-PLETS VIA DESSINS D’ENFANTS

We construct exponentially large collections of pairwise distinct equisingular deformation families of irreducible plane curves sharing the same sets of singularities. The fundamental groups of all curves constructed are abelian.

Some Obstructed Equisingular Families of Curves on Surfaces in P C

Very few examples of obstructed equsingular families of curves on surfaces other than P C are known. Combining results from [Wes04] and [Hir92] with an idea from [ChC99] we give in the present paper series of examples of families of irreducible curves with simple singularities on surfaces in P C which are not T–smooth, i.e. do not have the expected dimension, (Section 1) and we compare this wit...

The Geometry of Equisingular and Equianalytic Families of Curves on a Surface

Introduction The existence of singular algebraic curves with given invariants and given set of singular-ities and, at the same time, the study of (equisingular) families of such curves is a very old, but still attractive and widely open, problem. Already, at the beginning of the 20th century, the foundations were made in the works of Pl ucker, Severi, Segre and Zariski. In the sequel the theory...

New Asymptotics in the Geometry of Equisingular Families of Curves