Abstract
The group PGL(2) of linear transformations of the projective line acts
naturally on the d-dimensional projective space P^d parametrizing
configurations (`d-tuples') of points on the line. In this note we are
concerned with the orbits of this action of PGL(2) on P^d. The closure
of each orbit is a projective subvariety of P^d of which we determine
the degree, the `boundary'--i.e., the complement of an orbit in its
closure--, and the multiplicity at points of the boundary. These results
are used to provide a complete classification of the non-singular orbit
closures, and criteria for an orbit closure to be non-singular in
codimension 1.
Original language | English |
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Journal | Journal fur die Reine und Angewandte Mathematik |
Publication status | Published - 1993 |
Externally published | Yes |
Keywords
- Mathematics - Algebraic Geometry