ar X iv : m at h / 05 05 09 6 v 1 [ m at h . A G ] 5 M ay 2 00 5 THE PROJECTIVE INVARIANTS OF ORDERED POINTS ON THE LINE

ar X iv : m at h / 05 05 09 6 v 4 [ m at h . A G ] 7 N ov 2 00 5 THE PROJECTIVE INVARIANTS OF ORDERED POINTS ON THE LINE I

In this paper we study the structure of the graded ring of projective invariants of n ordered points on the projective line CP. A theorem of Kempe (1894) [Ke], see also [Howe] and [KR], states that the graded ring R of projective invariants is generated by elements of lowest degree. We give a new proof of this theorem using a toric degeneration. Our main theorem implies that the ideal of relati...

ar X iv : m at h / 05 05 09 6 v 2 [ m at h . A G ] 1 0 M ay 2 00 5 THE PROJECTIVE INVARIANTS OF ORDERED POINTS ONTHE LINE

In this paper we study the structure of the graded ring of projective invariants of n ordered points on the projective line CP. A theorem of Kempe (1894) [Ke], see also [Howe] and [KR], states that the graded ring R of projective invariants is generated by elements of lowest degree. We give a new proof of this theorem using a toric degeneration. Our main theorem implies that the ideal of relati...

ar X iv : m at h / 05 05 09 6 v 5 [ m at h . A G ] 1 0 N ov 2 00 5 THE PROJECTIVE INVARIANTS OF ORDERED POINTS ON THE LINE

In this paper we study the structure of the graded ring of pro-jective invariants of n ordered points on the projective line CP 1. A theorem of Kempe (1894) [Ke], see also [Howe] and [KR], states that the graded ring R of projective invariants is generated by elements of lowest degree. We give a new proof of this theorem using a toric degeneration. Our main theorem implies that the ideal of rel...

ar X iv : m at h / 06 05 35 5 v 1 [ m at h . G R ] 1 3 M ay 2 00 6 Axes in Outer Space

ar X iv : m at h / 05 04 08 2 v 4 [ m at h . D G ] 1 5 A pr 2 00 6 COMPLETE PROJECTIVE CONNECTIONS

The first examples of complete projective connections are uncovered: on surfaces, normal projective connections whose geodesics are all closed and embedded are complete. On manifolds of any dimension, normal projective connections induced from complete affine connections with slowly decaying positive Ricci curvature are complete.