7 research outputs found
On plane sextics with double singular points
We compute the fundamental groups of five maximizing sextics with double
singular points only; in four cases, the groups are as expected. The approach
used would apply to other sextics as well, given their equations.Comment: A few explanations and references adde
Plane sextics via dessins d'enfants
We develop a geometric approach to the study of plane sextics with a triple
singular point. As an application, we give an explicit geometric description of
all irreducible maximal sextics with a type singular point and
compute their fundamental groups. All groups found are finite; one of them is
nonabelian.Comment: a few points clarified; final version accepted for publicatio
Classical Algebraic Geometry
Algebraic geometry studies properties of specific algebraic varieties, on the one hand, and moduli spaces of all varieties of fixed topological type on the other hand. Of special importance is the moduli space of curves, whose properties are subject of ongoing research. The rationality versus general type question of these and related spaces is of classical and also very modern interest with recent progress presented in the conference. Certain different birational models of the moduli space of curves and maps have an interpretation as moduli spaces of singular curves and maps. For specific varieties a wide range of questions was addressed, including extrinsic questions (syzygies, the k-secant lemma) and intrinsic ones (generalization of notions of positivity of line bundles, closure operations on ideals and sheaves)