Varieties of clusters and Enriques diagrams

Details Varieties of clusters and Enriques diagrams Varieties of clusters and Enriques diagrams

2001-08-03

arxiv.org/abs/math/0108023v1

Mathematics

Algebraic Geometry

8 figures

Scientific paper

We study the geometry of the varieties of clusters X_r introduced by Kleiman
in the 70's, showing that for every Enriques diagram D of r vertices the subset
Cl(D) of the clusters with Enriques diagram D is locally closed. We study also
the relative positions of the subvarieties Cl(D), showing that they do not form
a stratification and giving criteria for adjacencies between them.

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