Linear orbits of d-tuples of points in P^1

Details Linear orbits of d-tuples of points in P^1 Linear orbits of d-tuples of points in P^1

1992-05-12

arxiv.org/abs/alg-geom/9205005v1

J. Reine Angew. Math. 445 (1993), 205-220

Mathematics

Algebraic Geometry

Tex dialect: `old' amstex 14 pages

Scientific paper

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.

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